Abstract For transport-reaction processes with certain general cost functions indicating comprehensive profit, the existing linear–quadratic optimal control or model predictive control (MPC) methods may be conservative. Due to their spatial characteristics, dynamic evolutions and final target static spatial distributions under different control strategies may result in remarkable variation of operation performance. This article presents a novel economic model predictive control (EMPC) synthesis for systems described by hyperbolic/parabolic partial differential equations (PDEs) with pre-optimized static spatially distributed profile, from both convergence and performance points of view. Instead of deriving approximate ordinary differential equations (ODEs) and applying finite-dimensional control strategies, this work addresses the optimization and stabilization problem on the basis of infinite dimensional model itself, which is realized by Cayley–Tustin (CT) transformation without any type of spatial approximation. The accumulated economic cost, input/output constraints are explicitly considered in the finite horizon optimal control problem (FHOCP), with an additional energy-like contractive constraint accounting for closed-loop convergence toward the target optimal steady-state profile. By directly solving Lyapunov functions associated with PDEs models, the parameters in the FHOCP are suitably defined such that the composite EMPC system admits algorithm feasibility and closed-loop stability. Finally, the proposed method is applied to typical examples; numerical results indicates the effectiveness and remarkable performance improvement of the EMPC method compared to standard MPC results.

中文翻译：

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具有目标剖面的传输反应系统的经济模型预测控制

摘要 对于具有某些表示综合利润的一般成本函数的输运反应过程，现有的线性-二次最优控制或模型预测控制（MPC）方法可能是保守的。由于它们的空间特性，不同控制策略下的动态演化和最终目标静态空间分布可能导致运行性能的显着变化。本文从收敛性和性能的角度，为由双曲线/抛物线偏微分方程 (PDE) 描述的系统提供了一种新颖的经济模型预测控制 (EMPC) 综合，具有预先优化的静态空间分布剖面。不是推导近似常微分方程 (ODE) 和应用有限维控制策略，这项工作在无限维模型本身的基础上解决了优化和稳定问题，这是通过 Cayley-Tustin (CT) 变换实现的，没有任何类型的空间近似。在有限范围最优控制问题 (FHOCP) 中明确考虑了累积的经济成本、输入/输出约束，并附加了一个类似能量的收缩约束，以实现闭环收敛到目标最优稳态曲线。通过直接求解与偏微分方程模型相关的李雅普诺夫函数，FHOCP 中的参数被适当地定义，使得复合 EMPC 系统承认算法的可行性和闭环稳定性。最后，将所提出的方法应用于典型的例子；