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This work addresses the problem of robust H ∞ model predictive control for constrained piecewise non-linear systems corrupted by norm-bounded disturbances for the first time. In this approach, the system can have different operating points with different subregions. In each subregion, the system is made up of an affine model disturbed by an additive non-linear term that is locally Lipschitz. The employment of the piecewise non-linear model leads to a non-convex optimization problem, which is far more difficult to solve. It is also much more challenging to develop the H ∞ model predictive control for piecewise non-linear systems. The proposed method introduces a control strategy in the form of a convex optimization problem subject to linear matrix inequality constraints, with the ability to minimize the L2 gain between the disturbance input and the controlled output. The proposed controller guarantees system stability with a prescribed H ∞ disturbance attenuation level under switching between subregions. Simulations on a highly non-linear chemical process are conducted to demonstrate the efficacy of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper studies the H∞ control problem for polynomial time‐varying systems. The H∞ control problem has been much less investigated for time‐varying systems in comparison to the time‐invariant systems. Approximate dynamic programming (ADP) is an optimal method to solve the control problems. Therefore, it is valuable to solve the polynomial time‐varying H∞ control problem with the ADP approach. Considering the time as an independent variable for sum‐of‐squares (SOS) optimization problems, an SOS‐based ADP method is proposed to solve this problem. A policy iteration algorithm is presented, where in its policy evaluation step it is sufficient to solve an optimization problem. Some constraints are added to this optimization problem to guarantee the closed‐loop exponential stability. The convergence and stability properties of the proposed algorithm are stated and proven. Moreover, in order to design an H∞ controller with a smaller disturbance attenuation coefficient, a two‐loop algorithm is suggested. Finally, the effectiveness of the proposed method is demonstrated by simulation examples. [ABSTRACT FROM AUTHOR]

In this paper, a decentralized energy management system is presented for intelligent microgrids with the presence of distributed resources using reinforcement learning. Due to the unpredictable nature of renewable energy resources, the variability of load consumption, and the nonlinear model of batteries, the design of a microgrid energy management system is associated with many challenges. In addition, centralized control structures in large-scale systems increase computational volume and complexity in control algorithms. In this paper, a fully decentralized multi-agent structure for a microgrid energy management system is proposed and the Markov decision process is used to model the stochastic behavior of agents in the microgrid. Electrical and thermal distributed resources, batteries, and consumers are considered intelligent and independent agents. They have the learning ability to explore and exploit the environment in a fully decentralized manner and achieve their optimal policies. The proposed method for hourly microgrid management is model-independent and based on learning. The method maximizes the profits of all manufacturers, minimizes consumer costs, and reduces the dependence of the microgrid on the maingrid. Finally, using real data from renewable energy sources and consumers, the accuracy of the proposed method in the Iranian electricity market is simulated and verified. [ABSTRACT FROM AUTHOR]

This paper proposes a tube‐based robust model predictive control (TMPC) scheme with an optimal tube for disturbance‐affected linear systems. In the literature on TMPC, there is no proper methodology to handle the considerable effects of the tube size on the closed‐loop system performance. There is usually a trade‐off between the disturbance rejection level and the amount of control effort available for the MPC problem. In some applications, it is nearly impossible to find a feasible TMPC to have a sufficient amount of states and inputs feasible sets for the MPC optimization problem. It would be a vital contribution to the TMPC designs if an algorithm is demonstrated which can investigate the suitability of TMPC for a specific system. This paper provides a solution for the mentioned challenges by introducing the concept of Quasi‐H∞ criterion and proposing a constrained optimization problem. The optimization problem is then reformulated and simplified to present an efficient methodology for the TMPC designers. The proposed TMPC scheme could benefit from a larger terminal region and result in a larger region of attraction. The achievements in TMPC designs are shown by simulations and comparisons with the previously used techniquesover numerical case studies. [ABSTRACT FROM AUTHOR]

In this article, the H∞ control problem is investigated for polynomial systems with uncertain parameters by utilising an adaptive dynamic programming (ADP) approach. The goal of this problem is to design a controller that stabilises the system and renders the system L2-gain less than some disturbance attenuation level for all possible values of the uncertain parameters. A policy iteration (PI) algorithm is proposed to approximately solve the Hamilton-Jacobi-Isaacs (HJI) equation based on the sum-of-squares (SOS) optimisation. The convergence of the iterative algorithm and robustness of the closed-loop system with respect to both external disturbances and parametric uncertainties are guaranteed. Moreover, a two-loop iterative algorithm is presented to design a parametric robust H∞ controller with a smaller L2-gain. The efficiency and advantage of the proposed SOS-based algorithm are demonstrated by simulation examples. [ABSTRACT FROM AUTHOR]

This paper investigates the suboptimal control design for polynomial time‐varying systems. It is known that the solution to this problem relies on the solution of the Hamilton–Jacobi–Bellman (HJB) equation, which is a nonlinear partial differential equation (PDE). A policy iteration (PI) algorithm is developed to solve the HJB equation. The policy evaluation step of this algorithm consists of a sum‐of‐squares (SOS) program, which is computationally tractable. This algorithm distinguishes from previously known SOS‐based adaptive dynamic programming (ADP) algorithms in that it is developed for time‐varying systems. The convergence of the iterative algorithm and the global stability of the closed‐loop system are proved. At the end, the effectiveness of the proposed algorithm is illustrated through two simulation examples. [ABSTRACT FROM AUTHOR]

This article considers the problems of robust stability and stabilization for a class of fractional-order linear time-invariant systems via 0<α<1 subject to input saturation with convex polytopic uncertainties, by a kind of H ∞ –proportional–integral–derivative control synthesis. A new saturation-based stability condition is suggested to estimate the stable region ( B ϵ ) and region of attraction (ε) using the ellipsoid approach. The main concept of the presented strategy is based on transforming the proportional–integral–derivative controller design problem into the static output feedback control problem. Gronwall–Bellman lemma and sector bounded condition of the saturation function is used for stability investigation and stabilization of such systems. The static output feedback control laws are obtained with the aid of a non-iterative linear matrix inequality implication. From the static output feedback controller, the proportional–integral–derivative controller is then restored. Stability problem is addressed as an optimization problem to obtain the controller gains and the stable region, as well as the largest region of attraction. Some theorems and numerical examples are provided to illustrate the results of proposed mechanism. [ABSTRACT FROM AUTHOR]