This paper proposes a novel geometry optimization strategy for the online robust active fault diagnosis (AFD) of discrete-time linear parameter varying (LPV) systems under set-theoretic framework. By establishing a bank of zonotopic set-value observers to match healthy/faulty system modes, the key of the optimization strategy comes down to the design of the optimal system inputs and gain matrices simultaneously

Privacy protection and nonconvexity are two challenging problems in decentralized optimization and learning involving sensitive data. Despite some recent advances addressing each of the two problems separately, no results have been reported that have theoretical guarantees on both privacy protection and saddle/maximum avoidance in decentralized nonconvex optimization. We propose a new algorithm for

This paper studies a linear-quadratic optimal control problem for discrete-time systems with multiplicative noise and random coefficients. Motivated by fiscal policy planning problems, where deterministic policies are required, this paper aims to find a deterministic optimal controller. The challenge is to seek a solution to forward and backward stochastic difference equations with structural inconsistency

In this work, we investigate the problem of privacy-preserving supervisory control against an external passive intruder via co-synthesis of a dynamic mask, an edit function, and a supervisor. We attempt to achieve the following goals: (1) the system secret cannot be inferred by the intruder, i.e., opacity of secrets against the intruder, and the existence of the dynamic mask and the edit function should

This paper discusses the problem of system identification when frequency domain side-information is available. We mainly consider the case where the side-information is provided as the H∞-norm of the system being bounded by a given scalar. This framework allows considering different forms of frequency domain side-information, such as the dissipativity of the system. We propose a nonparametric identification

Stochastic optimal control usually requires an explicit dynamical model with probability distributions, which are difficult to obtain in practice. In this work, we consider the linear quadratic regulator (LQR) problem of unknown linear systems and adopt a Wasserstein penalty to address the distribution uncertainty of additive stochastic disturbances. By constructing an equivalent deterministic game

In this paper, we propose time-discounted schemes for full information estimation (FIE) and moving horizon estimation (MHE) that are robustly globally asymptotically stable (RGAS). We consider general nonlinear system dynamics with nonlinear process and output disturbances that are a priori unknown. For FIE being RGAS, our only assumptions are that the system is time-discounted incrementally input

This paper is concerned with the data-driven optimal control of nonlinear systems. We present a convex formulation of the optimal control problem with a discounted cost function. We consider optimal control problems with both positive and negative discount factors. The convex approach relies on lifting nonlinear system dynamics in the space of densities using the linear Perron–Frobenius operator. This

This paper deals with the robust stabilization of uncertain discrete-time switched affine systems using a control Lyapunov approach and a min-switching state-feedback control law. After presenting some preliminaries on limit cycles, a constructive stabilization theorem, expressed as linear matrix inequalities, guarantees that the solutions to the nominal closed-loop system converge to a limit cycle

This paper considers the state estimation problem for nonlinear dynamic systems with unknown but bounded noises. Set membership filter (SMF) is a popular algorithm to solve this problem. In the set membership setting, we investigate the filter problem where the state estimation requires to be constrained by a linear or nonlinear equality. We propose a consensus alternating direction method of multipliers

We analyse the turnpike properties for a general, infinite dimensional, linear–quadratic (LQ) optimal control problem, in both the deterministic and the parameter dependent case. The novelty of the paper is twofold. Firstly, it obtains positive turnpike results for systems that are (partially) uncontrollable. Secondly, it provides turnpike results for optimal averaged control associated to a family

The control of multiple magnetic microrobots is of particular interest for therapeutic applications. Yet the controllability of such a system is not straightforward since, on most of such systems designs, there is only a single control input per axis. The paper addresses the controllability and control synthesis for several magnetic microrobots navigating in blood vessels. First, controllability requires

This paper studies the dynamic event-triggered intermittent control (D-ETIC) for the stabilization of delayed dynamical systems (DDS). The stabilization of DDS via general intermittent control is formulated as a problem of delay-dependent minimal activation time rate (MATR). A D-ETIC scheme with input delay is proposed to stabilize DDS. The delay-dependent MATR is estimated. And the maximal input delay

Discarding constraints in scenario optimization, a technique known as the sampling-and-discarding scheme, allows the decision maker to trade feasibility to performance. Recently, a removal scheme with a less conservative bound on the constraint violation probability of the final decision has been proposed. In this letter, we further contribute to the theoretical properties of such a scheme by extending

This paper solves the problem of exact computation of the phase and gain margins of multivariable control systems. These stability margins are studied using the concept of the Davis–Wielandt shell of complex matrices. Calculation of the phase and gain margins requires solving a quadratically constrained quadratic program (QCQP) and a parametrized quadratically constrained problem, respectively, which

This paper applies the method of backward stochastic differential equations (BSDEs) to study the bang–bang optimal stochastic control problem, where the optimal control is of the feedback form and the final cost functional is given by a symmetric function. In addition to obtaining the existence of the optimal control, we also give the explicit representation of the optimal control and the optimal value

We investigate the problem of optimally observing a finite set of targets using a mobile agent over an infinite time horizon. The agent is tasked to move in a network-constrained structure to gather information so as to minimize the worst-case uncertainty about the internal states of the targets. To do this, the agent has to decide its sequence of target-visits and the corresponding dwell-times at

For a class of state-constrained dynamical systems described by evolution variational inequalities, we study the time evolution of a probability measure which describes the distribution of the state over a set. In contrast to smooth ordinary differential equations, where the evolution of this probability measure is described by the Liouville equations, the flow map associated with the nonsmooth differential

The advances in data science and machine learning have resulted in significant improvements regarding the modeling and simulation of nonlinear dynamical systems. It is nowadays possible to make accurate predictions of complex systems such as the weather, disease models or the stock market. Predictive methods are often advertised to be useful for control, but the specifics are frequently left unanswered

In this work, we address the leader-following consensus problem of multi-agent systems by developing a novel reset consensus protocol with a time-varying gain matrix. The reset consensus protocol is distinct from existing results in the sense that it integrates a high-dimensional element with the reset actions triggered by a prescribed reset band. After converting the original closed-loop system to

Finite-time control owns the advantages of precision and rapidness, preferred by many applications with high performance requirements. Its realization calls for subtle treatments, e.g., the Lyapunov method with low-order terms and homogeneity with negative degree. However, the methods available for finite-time control are based on some basic exclusions and essential restrictions to system uncertainties

This paper studies system identification of ARMA models with binary-valued observations. Compared with existing quantized identification of ARMA models, this problem is more challenging since the accessible information is much less. Different from the identification of FIR models with binary-valued observations, the prediction of original system output and the parameter both need to be estimated in

Assuming the uncertain parameter of a linear polytopic system to be uniformly distributed, we can prove that the system is almost sure exponentially stable if and only if its averaging system is stable. Computing the mathematical expectation of the state-transition matrix and characterizing the martingale structure embedded in its variance is the key for deriving this stability criterion.

In this brief, continuous-time nonlinear systems with extended matching uncertainties are considered. The problem of designing a state-feedback adaptive learning control of reduced complexity — just including a single adaptive learning estimation scheme in the upper subsystem and a high-gain proportional action in the input channel — is addressed. By properly setting the control parameters, exponential

We study an inverse problem of the stochastic optimal control of general diffusions with performance index having the quadratic penalty term of the control process. Under mild conditions on the system dynamics, the cost functions, and the optimal control process, we show that our inverse problem is well-posed using a stochastic maximum principle. Then, with the well-posedness, we reduce the inverse

In this paper, we investigate the algorithm of distributed optimization and control for task-space bipartite coordination of multiple uncertain Lagrange plants (MULPs) with unavailable dynamical parameters. We establish the global cost function based on the sum of the user-defined local cost functions, which are respectively presented for all the individuals within the MULPs. We present a hierarchical

We propose a framework for designing global observers for nonlinear systems with disturbances under geometric conditions based on orbital symmetries. Under some additional restrictions these orbital symmetry-based conditions boil down to geometric homogeneity (at infinity) conditions. Our observers are the result of the combination of a first filter, a state norm estimator, with a second filter adaptively

ω-limit set can be used to understand the long term behavior of a dynamical system. In this paper, we use the Lyapunov Function PDEs method, developed in our previous work, to study the relation between ω-limit points and boundaries for chemical reaction networks equipped with mass-action kinetics. Using the solution of the PDEs, some new checkable criteria are proposed to diagnose non ω-limit points

This paper is concerned with the problem of self-triggered multi-mode control for a class of Markovian jump systems, in which the system states are transmitted to the controller via a communication network with limited bandwidth. In order to achieve the desired performance of the closed-loop system via utilizing a controller with fewer modes, a mode monitoring mechanism related to the system modes

In this paper we are interested in the problem of state observation of state-affine nonlinear systems. It is well-known that observability of the system is a necessary assumption for the state reconstruction. Our main contribution is to prove that it is also sufficient to design a globally exponentially stable observer This should be contrasted with existing results that require the strictly stronger

We solve the output-feedback stabilization problem for a tank with a liquid modeled by the viscous Saint-Venant PDE system. The control input is the acceleration of the tank and a Control Lyapunov Functional methodology is used. The measurements are the tank position and the liquid level at the tank walls. The control scheme is a combination of a state feedback law with functional observers for the

In this paper, we address the problem of cooperative tracking of multiple heterogeneous targets by deploying multiple and heterogeneous pursuers exhibiting different decision-making capabilities. Initially, under infinite resources, we formulate a game between the evader and the pursuing team, with an evader being the maximizing player and the pursuing team being the minimizing one. Subsequently, we

The problem of synchronization and balancing around simple closed polar curves is addressed for unicycle-type multi-agent systems. Leveraging the concept of barrier Lyapunov function in conjunction with bounded Lyapunov-like curve-phase potential functions, we propose distributed feedback control laws and show that the agents asymptotically stabilize to the desired closed curve in synchronized and

This paper deals with the estimation of the hidden factor in Dynamic Generalized Factor Analysis via a generalization of Kalman filtering. Asymptotic consistency is discussed and it is shown that the Kalman one-step predictor is not the right tool while the pure filter yields a consistent estimate.

A multi-defender single-invader target defense game is a differential game where the invader intends to enter a target area protected by a group of defenders, while the defenders intend to capture the invader before it enters. This game has been extensively studied and a geometric solution exists. However, this solution has only been justified under special cases. The main contribution of this paper

In this note, we consider a class of homogeneous second order systems which contains two relevant sub-classes: the first one in a controller form and the second one in an observer form. For both of them, we provide necessary and sufficient conditions on the gain parameters to guarantee oscillatory or non-oscillatory behavior of the solutions. This is in the same spirit of tuning of second order linear

This paper studies the control of a generic longitudinal air vehicle dynamic model during the cruise phase with nonlinearly parametrized uncertain aerodynamic functions. Verified by the improved coefficient precision of the aerodynamic forces and moments, using a curve fitting technique on available flight data, it is demonstrated that a nonlinearly parametrized model can more accurately capture the

In this paper we consider state-feedback global stabilization of a semilinear 1D heat equation with a nonlinearity exhibiting a linear growth bound. We study both non-local and boundary control via a modal decomposition approach. For both cases, we suggest a direct Lyapunov method applied to the full-order closed-loop system. The nonlinear terms are compensated by using Parseval’s inequality, leading

This paper studies the mean-square stability of discrete-time linear switched systems with random switching, where the switching signal is the output of a logic dynamical switching model driven by an independent and identically distributed (i.i.d.) process. This class of switching is referred to as the modeled random switching. By regarding the switching model as a part of the system, a combined switched

In this paper, an uncertain nonlinear switched system is a nonlinear switched system disturbed by subjective uncertainties, which can be formulated by several uncertain differential equations. Few results concerning such type of nonlinear switched systems were published before. To fill this gap, the property of solutions for uncertain nonlinear switched systems with finite-time horizon is discussed

As one of attitude representation methods for a rigid body, the rotation matrices defined on the special orthogonal matrix group SO(3) can give the unique, global and nonsingular solution. For the attitude control systems evolving on Lie group SO(3)×R3, a second-order sliding surface is constructed and proved to be a Lie subgroup, along which the reduced-order dynamics is almost globally asymptotically

This paper investigates the impact of addition/removal/reweighting of edges in a complex networked linear control system. For networks of positive edge weights, we show that when adding edges leads to the creation of new cycles, these in turn may lead to instabilities. Dynamically, these cycles correspond to positive feedback loops. Conditions are provided under which the modified network is guaranteed

A suboptimal approach to distributed NMPC is proposed based on Gaussian process models of the interconnected systems dynamics and taking into account the imposed constraints. The suggested method is based on a sequential linearization of the nonlinear system dynamics and finding a suboptimal solution of the resulting Quadratic Programming (QP) problem by using distributed iterations of the dual accelerated

In this paper, the stabilization problem of networked systems with communication constraints is studied, where the random sampling periods, deception attacks and packet losses are considered simultaneously. Different from the existing literature, the actual sampling periods are subject to undesirable physical constraints and fluctuate around an ideal sampling period with certain probability distribution

In this paper we investigate the herdability property, namely the capability of a system to be driven towards the (interior of the) positive orthant, for linear time-invariant state space models. Herdability of certain matrix pairs (A,B), where A is the adjacency matrix of a multi-agent network, and B a selection matrix that singles out a subset of the agents (the “network leaders”), is explored. The

In this paper, a relative degree two (RD2) sliding variable based discrete time sliding mode control (DTSMC) is designed for a linear time invariant system when output sampling is done faster than control input computation. The RD2 framework has been established for better performance and improved robustness of the discrete time sliding mode control system. The paradigm of fast output sampling (FOS)

We consider the problem of ensuring stability in a DC microgrid by means of decentralized conditions. Such conditions are derived which are formulated as input–output properties of locally defined subsystems. These follow from various decompositions of the microgrid and corresponding properties of the resulting representations. It is shown that these stability conditions can be combined together by

Reduction theorems provide a framework for stability analysis that consists in breaking down a complex problem into a hierarchical list of subproblems that are simpler to address. This paper investigates the following reduction problem for time-varying ordinary differential equations on Rn. Let Γ1 be a compact set and Γ2 be a closed set, both positively invariant and such that Γ1⊂Γ2⊂Rn. Suppose that

The normal form, which is also known as Byrnes–Isidori normal form, of a linear system is very important in control theory, as it is a fundamental tool for solving a couple of important problems. It is known that the normal form exists only if the system has a relative degree and a nonsingular coupling matrix, which is not always satisfied. Though both the relative degree and the non-singularity of

The problem of designing a stabilizing feedback controller in the presence of saturating actuators and multi-rate (asynchronous) aperiodic state measurements is studied. Specifically, we consider a scenario in which measurements of the plant states are collected at the controller end in a sporadic and asynchronous fashion. A hybrid controller is used to perform a fusion of measurements sampled at different

This paper considers general heterodirectional linear hyperbolic PDEs with boundary actuation and collocated measurement, that are bidirectionally coupled with nonlinear ODEs at the unactuated boundary. An output feedback regulator is designed to have the control output track a reference in the presence of disturbances, with a nonlinear signal model generating the reference and the disturbances. This

It is shown that the claim (i) of Theorem 13 in the commented article is actually not true, i.e., there does not always exist a (s+1)th order retarded type input–output equation for a nonlinear time-delay system with observability index s. For some special cases the existence of a retarded type input–output equation is described.

In this paper, we propose a decoupled approach to the design of a robust sliding mode observer. The proposed observer has a linear part, which is designed based on the linear observer theory, and a discontinuous part based on the sliding mode technique to reject the disturbance signals. Here, the discontinuous injection of output error is fed only to the sliding mode part of the observer, whereas the

This paper studies an optimal tuning of the boundary controller for a heterogeneous traffic flow model with disturbances in order to alleviate congested traffic. The macroscopic first-order N-class Aw–Rascle traffic model consists of 2N hyperbolic partial differential equations. The vehicle size and the driver’s behavior characterize the type of vehicle. There are m positive characteristic velocities

This paper studies optimal linear quadratic regulation (LQR) problem of discrete-time interconnected systems (ISs) defined over a weakly connected graph. Subsystems in an IS share information based on the topology of the system. The main challenge of this work in comparison to the standard LQR problem, stems from that a subsystem may never acquire information from some other subsystems, due to the

The Back Propagation (BP) neural network model is one of the neural network models suitable for model recognition and classification. However, a single BP network model cannot fully tap the feature information hiding in the data and is vulnerable to the uncertainty associated with system parameter changes and also suffers from the effects of long diagnosis times, inaccurate and undesired diagnosis

Recently, a constructive method for the finite-dimensional observer-based control of deterministic parabolic PDEs was suggested by employing a modal decomposition approach. In this paper, for the first time we extend this method to the stochastic 1D heat equation with nonlinear multiplicative noise. We consider the Neumann actuation and study the observer-based as well as the state-feedback controls

This study proposes an adaptive quantized fault-tolerant control for a nonlinear two-degree of freedom (2-DOF) helicopter system with an unknown dead zone and actuator failures. First, a hysteresis quantizer is employed to reduce the jittering during signal quantization. Second, a radial basis function neural network is adopted to address the uncertainty in the nonlinear helicopter system. Bounded

The sequential compactness afforded hybrid systems under mild regularity constraints guarantee outer/upper semicontinuous dependence of solutions on initial conditions and perturbations. For reachable sets of hybrid systems, this property leads to upper semicontinuous dependence with respect to initial conditions, time, and perturbations. Motivated by these results, we define a counterpart to sequential

In the contest of optimal control problems, regularity results for optima are known when addressing fiber-strictly convex Lagrangian. For infinite time horizons, or for settings with infinite dimensional dynamics, the equivalence between minima/maxima and extremals could break down. Commonly, this is due to a loss of convexity/concavity of the cost functional or to a presence of state constraints,