We consider a version of the pole placement problem for continuous time-varying linear systems. Our purpose is to prove that uniform complete controllability is equivalent to possibility of arbitrary assignment of the dichotomy spectrum. The main ingredients of the proof are the reduction of system to upper triangular form and the use of the concept of uniform complete stabilization. To illustrate

While presenting many advantages in application, the loss of actuators also brings about great challenge to the control of underactuated systems. Specifically, the unactuated DOFs (degrees of freedom) cannot be directly controlled, instead, they have to be stabilized indirectly through appropriate regulation of actuated ones. As an unfortunate fact, the natural couplings between actuated and unactuated

In this paper, methods of commutator calculus are used to study stability and stabilization for periodic linear systems. Asymptotic stability is investigated using a quadratic Lyapunov function, whose matrix is a piecewise-exponential approximation of the solution of the differential Lyapunov matrix equation. Algorithm for constructing a stabilizing control in the form of linear feedback, dependent

We consider linear open quantum systems with passive Hamiltonians and a single, local dissipative process. Generally speaking, these systems are easier to implement than systems with active Hamiltonians and non-local dissipative processes. We parametrize the set of all covariance matrices corresponding to pure Gaussian steady states that can be achieved by this type of quantum system. Given such pure

This paper proposes a generalized set-theoretic interval observer (GSIO) for robust state estimation of discrete linear time-invariant (LTI) systems with bounded uncertainties. Including the previous set-theoretic interval observer (SIO) as a special case, the proposed GSIO only requires to transform the system matrix of the first subsystem to be nonnegative. Based on this idea, a nonsmooth H∞ optimization

In this paper, a switched control method for a class of wearable robotic systems that prioritizes the use of human skeletal muscles in an assistive rigid powered exoskeleton is derived. A general N-degree-of-freedom (N-DOF) human–robot model is proposed to consider the challenges induced by the wearable system that include uncertainties and nonlinearities, unilateral actuation properties of the skeletal

Probabilistic guarantees of safety and performance are important in constrained dynamical systems with stochastic uncertainty. We consider the stochastic reachability problem, which maximizes the probability that the state remains within time-varying state constraints (i.e., a “target tube”), despite bounded control authority. This problem subsumes the stochastic viability and terminal hitting-time

Previous work on controllability of underactuated serial horizontal planar manipulators mostly focused only on a specific number of links, whereas this paper considers a general N-link case. The main contribution of this paper is accessibility and small-time local controllability (STLC) results for N-link serial, horizontal, planar manipulators with one unactuated joint. An N-link (N≥3) manipulator

This paper deals with new finite-time estimation algorithms for Linear Parameter Varying (LPV) discrete-time systems and their application to output feedback stabilization. Two exact finite-time estimation schemes are proposed. The first scheme provides a direct and explicit estimation algorithm based on the use of delayed outputs, while the second scheme uses two combined asymptotic observers, connected

In this paper, we consider an estimation problem of invariant nonlinear systems subject to dynamic additive disturbances. We identify two sets of sufficient conditions that preserve the invariant properties of the systems under the disturbances. We apply the conditions to a unicycle model under linear dynamic disturbances and design two different Invariant Extended Kalman filters (IEKFs). Both IEKFs

We first propose a class of generalized homogeneous vector fields which include existing ones as special cases. Then we establish a necessary and sufficient condition for D-stability of more general homogeneous cooperative systems. The decay rate is also explicitly estimated. Two numerical examples are worked out to show the effectiveness of the main result.

This paper proposes new robust nonlinear optimal control formulations in the weighted Sobolev space, here called nonlinear W2 and W∞ controllers, to handle with two classes of underactuated mechanical systems: the reduced ones with a reduced number of DOF; and the entire underactuated mechanical systems with input coupling. The optimal control problems are formulated via dynamic programming and particular

This paper considers global optimization of a continuous nonconvex piecewise affine (PWA) function over a polytope. This type of optimization problem often arises in the context of control of continuous PWA systems. In literature, it has been shown that the given problem can be formulated as a mixed integer linear programming (MILP) problem, the worst-case complexity of which grows exponentially with

In the context of control and estimation under information constraints, restoration entropy measures the minimal required data rate above which the state of a system can be estimated so that the estimation quality does not degrade over time and, conversely, can be improved. The remote observer here is assumed to receive its data through a communication channel of finite bit-rate capacity. In this paper

In this paper, we investigate a sparse optimal control of continuous-time stochastic systems. We adopt the dynamic programming approach and analyze the optimal control via the value function. Due to the non-smoothness of the L0 cost functional, in general, the value function is not differentiable in the domain. Then, we characterize the value function as a viscosity solution to the associated Hamilton–Jacobi–Bellman

This paper addresses the problem of estimating the attitude of a robotic platform using biased measurements of: (i) the direction of the gravitational field and (ii) angular velocity obtained from a set of high-grade gyroscopes sensitive to the Earth’s rotation. A cascade solution is proposed that features a Kalman filter (KF) tied to a rotation matrix observer built on the special orthogonal group

This paper explains a technical problem in the main theorem of the well-known paper “Finite-time and fixed-time stabilization: implicit Lyapunov function approach” by Polyakov et al. (2015), which makes impossible to fulfill one of its conditions for the class of disturbances therein specified, thus rendering void its supposed applicability and advantages over ordinary sliding mode methodologies.

This paper is concerned with functional observer-based finite-time adaptive integral sliding mode control (ISMC) for continuous systems with unknown nonlinear function. First, a novel finite-time ISMC framework is established based on the functional observer whose parameters can be directly found. Second, an adaptive compensator is designed to counteract the effect of the unknown nonlinear function

Developing efficient computational methods to assess the impact of external interventions on the dynamics of a network model is an important problem in systems biology. This paper focuses on quantifying the global changes that result from the application of an intervention to produce a desired effect, which we define as the total effect of the intervention. The type of mathematical models that we will

Using multiple saturations and delays, we present a time-domain static output feedback control approach for global stabilization of a chain of integrators with input constraints. In lieu of estimating the state by observers, we utilize the output with distinct delays to construct static output feedback control laws. A nested saturation design technique is employed to handle the nonlinearity in the

This paper describes a novel passivity/dissipativity based approach for fault tolerant control (FTC) of nonlinear systems by means of fault hiding, i.e., by inserting reconfiguration blocks (RBs) between the plant and controller to mitigate the fault effects. The proposed approach is used to design a new kind of RB, called passivation block (PB), which is generically employed for sensor and actuator

Quantum entanglement plays a fundamental role in quantum computation and quantum communication. Feedback control has been widely used in stochastic quantum systems to generate given entangled states since it has good robustness, where the time required to compute filter states and conduct filter-based control usually cannot be ignored in many practical applications. This paper designed two control

In least costly experiment design, the optimal spectrum of an identification experiment is determined in such a way that the cost of the experiment is minimized under some accuracy constraint on the identified parameter vector. Like all optimal experiment design problems, this optimization problem depends on the unknown true system, which is generally replaced by an initial estimate. One important

In this paper, we provide a decentralized theoretical framework for coordination of connected and automated vehicles (CAVs) at different traffic scenarios. The framework includes: (1) an upper-level optimization that yields for each CAV its optimal time trajectory and lane to pass through a given traffic scenario while alleviating congestion; and (2) a low-level optimization that yields for each CAV

This paper presents a sufficient condition and its certification algorithm for solving box-constrained linear model predictive control (MPC) problems within a certain number of iterations equal to the number of constrained prediction points. For implementing a model predictive controller in industrial applications, it is crucial to guarantee a concrete upper bound on the computational load so that

This paper is concerned with the cooperative output regulation problem for a network of agents with different dynamics described by parabolic PDEs subject to spatially- and time-varying parameters. Firstly, a networked controller is designed achieving output synchronization for identical finite-dimensional reference models, which deliver the state of the global reference model required for the synchronization

For linear time-invariant time delay systems, the so-called Lyapunov–Krasovskii functionals of complete type (Kharitonov and Zhabko, 2003) are known to be effective in the stability analysis and a number of applications. More precisely, there exist the necessary and sufficient asymptotic stability and instability conditions expressed in terms of these functionals. The case excluded from consideration

We study a distributed decision-making problem in which multiple agents face the same multi-armed bandit (MAB), and each agent makes sequential choices among arms to maximize its own individual reward. The agents cooperate by sharing their estimates over a fixed communication graph. We consider an unconstrained reward model in which two or more agents can choose the same arm and collect independent

A Discrete Event System (DES) modeled by a Petri Net (PN) is live if it is possible to fire any transition, although not necessarily immediately, from any marking that is reachable from the initial marking. A Liveness Enforcing Supervisory Policy (LESP) for a PN enforces liveness by preventing the firing of a subset of transitions called the controllable transitions, which correspond to the preventable

We consider the problem of computing the maximal invariant set of discrete-time linear systems subject to a class of non-convex constraints that admit quadratic relaxations. These non-convex constraints include semialgebraic sets and other smooth constraints with Lipschitz gradient. With these quadratic relaxations, a sufficient condition for set invariance is derived and it can be formulated as a

This paper introduces a novel method, namely the approximations of Lyapunov functionals, for input-to-state stability (ISS) analysis of a class of higher dimensional nonlinear parabolic partial differential equations (PDEs) with variable coefficients. Specifically, for any q∈[1,+∞] and the considered nonlinear parabolic PDEs with different types of boundary disturbances in Llocq(R+;L1(∂Ω)) and initial

This paper revisits a well studied leader-following consensus problem of linear multi-agent systems, while aiming at follower nodes’ transient performance. Conventionally, when not all follower nodes have access to the leader’s state information, distributed observers are designed to estimate the leader’s state, and the observers are coupled via communication network. Then each follower node only needs

In this paper, it is shown that a simple formulation of Economic Model Predictive Control can be used which possesses two features that are generally viewed as mutually exclusive, namely, a rather short prediction horizon (reachability-compatible) on one side, and the absence of final constraint on the other side. Practical stability at an arbitrarily small neighborhood of the optimal unknown steady-state

This note introduces, and studies, the Minkowski–Bellman inequality and equation. The necessary and sufficient conditions for the characterization and existence of Minkowski functions that satisfy the Minkowski–Bellman inequality, and for the characterization and existence of the unique Minkowski function that satisfies the Minkowski–Bellman equation, are derived. The complete topological characterization

In this paper we estimate the minimal controllability time for a class of non-linear control systems with a bounded convex state constraint. An explicit expression is given for the controllability time if the image of the control matrix is of co-dimension one. A lower bound for the controllability time is given in the general case. The technique is based on finding a lower dimension system with the

In this brief, a surplus-based approach is proposed to solve the distributed optimal resource allocation problem over directed graphs. Two features distinguish our method from the existing distributed resource allocation schemes. The first one is that the proposed method can be implemented on general strongly connected graph and overcomes the asymmetry caused by the digraphs. The second one is that

For fuzzy systems, it is known that membership function dependent Lyapunov function can reduce the conservatism that has arisen from quadratic Lyapunov function but the time derivative of membership function is hard to be dealt with. In this technical paper, a kind of generalized Lyapunov function (called homogeneous polynomially membership functions dependent (HPMFD) Lyapunov function ) is designed

We study the problem of synthesizing a control strategy to enforce safety of affine-in-control stochastic dynamical systems over finite time horizons. We use stochastic control barrier functions to quantify the probability that a system exits a given safe region of the state space in finite-time and consider both continuous-time and discrete-time systems. A barrier certificate condition that bounds

We propose two perturbation-based extremum seeking control (ESC) schemes for general single input single output nonlinear dynamical systems, having structures similar to that of the classical ESC scheme. We propose novel adaptation laws for the excitation signal amplitudes in each scheme that drive the amplitudes to zero. The rates of decay for both the laws are governed by the gradient measures of

The paper deals with the global asymptotic stability of general nonlinear time-delay systems with delay-dependent impulses through the Lyapunov–Krasovskii method. We derive a unified stability criterion which can be applied to a variety of impulsive systems. The cases when each of the continuous dynamics and the impulsive component is either stabilizing or destabilizing are investigated. Both theoretically

We present a novel distributionally robust optimization approach for integrated design and assessment of fault detection system. Its salient feature is the guaranteed robustness against the inexactness of probability distribution of unknown disturbances. The integrated design problem is formulated as a distributionally robust chance constrained program (DRCCP). It maximizes fault detectability subject

This article introduces, and studies, the robust control Minkowski–Lyapunov inequality, which is a natural generalization of the recently introduced control Minkowski–Lyapunov inequality. The generalization considers the setting of parametrically uncertain linear discrete time systems. The necessary and sufficient conditions for the characterization and existence of Minkowski functions that verify

This paper proposes a new lexicographic multi-objective model predictive control (MoMPC) scheme for constrained nonlinear systems with changing objective prioritization. The lexicographic optimization-based receding horizon optimal control problem is firstly formulated to accommodate the concern on prioritized control of multiple (economic) objectives. Then an elaborate generic function and the notion

We study a security problem for interconnected systems, where each subsystem aims to detect local attacks using local measurements and information exchanged with neighboring subsystems. The subsystems also wish to maintain the privacy of their states and, therefore, use privacy mechanisms that share limited or noisy information with other subsystems. We quantify the privacy level based on the estimation

We study the distributed model predictive control (DMPC) problem for a network of linear discrete-time subsystems in the presence of stochastic noise among communication channels, where the system dynamics are decoupled and the system constraints are coupled. The DMPC is cast as a stochastic distributed consensus optimization problem by modeling the exchanged variables as stochastic ones and a novel

This paper presents an online estimation method for highly nonlinear systems. This method fits the data to a nonlinear in the parameters regression model, where each parameter is an unknown function of known variables that we call causal regressors. We define this model as an Autoregressive with eXogenous inputs and Causal-regressors-Dependent Parameters (ARX-CDP) model. We are interested on modeling

The potential of a decentralized/distributed system to behave intelligently as a whole hinges on the capacity of its constituents to exchange and process information. In sensor networks and multiagent platforms this may be realized by means of distributed information fusion techniques. The very nature of these approaches demands specifying, or at least approximating, the statistical interdependencies

In this article, we consider the design of an event-triggered ℓ2-control policy, for a setting where a scheduler is arbitrating state transmissions from the sensors to the controller of a discrete-time linear system. We start by introducing a periodic time-triggered ℓ2-controller for different transmission time-periods with a given ℓ2-gain bound using the minimax game-theoretical approach. After that

The identification of switched systems is a challenging problem, which entails both combinatorial (sample-mode assignment) and continuous (parameter estimation) features. A general framework for this problem has been recently developed, which alternates between parameter estimation and sample-mode assignment, solving both tasks to global optimality under mild conditions. This article extends this framework

Output global finite-time stability of locally Lipschitz continuous autonomous systems is characterized by means of smooth Lyapunov functions. The so-called output-Lagrange stable systems are studied with details. Influence of a kind of continuity of the settling-time function is considered. Necessary and sufficient conditions of output finite-time stability are presented. The theoretical results are

In this paper, a tractable sampled-data controller synthesis method is proposed for linear time-invariant plants that gives guarantees for stability and performance of the closed-loop system in terms of the H∞- and H2-norm. This is done by taking a so-called jump/hybrid systems approach, which allows formulating linear matrix inequalities using an explicit solution to the Riccati differential equation

In this paper, we focus on the study of quotients of Boolean control networks (BCNs) with the motivation that they might serve as smaller models that still carry enough information about the original network. Given a BCN and an equivalence relation on the state set, we consider a labeled transition system that is generated by the BCN. The resulting quotient transition system then naturally captures

This paper deals with sliding mode control for networked Markovian jump systems with partially-known transition probabilities via an event-triggered scheme to reduce network bandwidth usage and save network resources. First, based on the analysis of event-triggered scheme and sliding mode control, a corresponding time-delay system model is constructed by investigating the effect of the network transmission

We investigate notions of network centrality in terms of the underlying coupling graph of the network, structure of exogenous uncertainties, and communication time-delay. Our focus is on time-delay linear consensus networks, where uncertainty is modeled by structured additive noise on the dynamics of agents. The centrality measures are defined using the H2-norm of the network. We quantify the centrality

The design of a position observer for the interior permanent magnet synchronous motor is a challenging problem that, in spite of many research efforts, remained open for a long time. In this paper we present the first globally exponentially convergent solution to it, assuming that the saliency is not too large. As expected in all observer tasks, a persistency of excitation condition is imposed. Conditions

We analyse a differential game with spatially distributed controls to study a multiregional transboundary pollution problem. The dynamics of the state variable (pollution stock) is defined by a two dimensional parabolic partial differential equation. The control variables (emissions) are spatially distributed variables. The model allows for a, possibly large, number of agents with predetermined geographical

In this paper, the combination of the attitude synchronization and rigid formation problem of multiple moving rigid bodies are considered. The moving rigid bodies communicate with each other via a distance-dependent interaction network, yielding the dynamical neighbor relations and the coupling relationship between positions and attitudes of all rigid bodies. The finite-time control and potential function

The adaptive distributed observer approach has been an effective tool for synthesizing a distributed control law for solving various control problems of leader–follower multiagent systems. However, the existing adaptive distributed observer needs to make use of the full state of the leader system. This assumption not only precludes many practical applications in which only the output of the leader

This paper deals with M2-signals, namely multivariate (or vector-valued) signals defined over a multidimensional domain. In particular, we propose an optimization technique to solve the covariance extension problem for stationary random vector fields. The multidimensional Itakura–Saito distance is employed as an optimization criterion to select the solution among the spectra satisfying a finite number

This paper solves finite-time stabilization problem of stochastic low-order nonlinear systems with time-varying orders and stochastic inverse dynamics. Due to stochastic low-order systems being merely continuous but not smooth, and the appearance of time-varying orders and stochastic inverse dynamics, all of control methods of stochastic nonlinear systems are inapplicable. By characterizing unmeasured