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Abstract: This paper is concerned with the high-performance robust control of discrete-time linear time-invariant (LTI) systems with semi-algebraic uncertainty regions. It is assumed that a robustly stabilizing static controller is given whose gain depends polynomially on the uncertain variables. The problem of tuning this parameter-dependent gain with respect to a prescribed quadratic cost function is formulated as a sum-of-squares (SOS) optimization. This method leads to a near-optimal controller whose performance is better than that of the initial controller. It is shown that the results derived in the present work encompass the ones obtained in a recent paper. The efficacy of the results is elucidated by an example. [Copyright &y& Elsevier]

This paper considers a class of generalized convex games where each player is associated with a convex objective function, a convex inequality constraint and a convex constraint set. The players aim to compute a Nash equilibrium through communicating with neighboring players. The particular challenge we consider is that the component functions are unknown a priori to associated players. We study two distributed computation algorithms and analyze their convergence properties in the presence of data transmission delays and dynamic changes of network topologies. The algorithm performance is verified through demand response on the IEEE 30-bus Test System. Our technical tools integrate convex analysis, variational inequalities and simultaneous perturbation stochastic approximation. [ABSTRACT FROM AUTHOR]

Abstract: This paper studies the fundamental problems: whether an affine system affected by additive disturbances is robustly transferable from a source set (simplex) to a target set (polytope) and whether it is robustly stabilizable with its state constrained in a simplex. First, a necessary and sufficient condition is derived for the existence of affine feedback control that solves the robust reachability problem. Further investigation is provided for two situations relying on whether the union of the source set and the target set is convex or non-convex. For the former one, a necessary and sufficient condition is obtained in the form of linear inequalities, while for the latter, several computationally feasible sufficient conditions are found. Second, we show that robust stabilization subject to a state constraint is equivalent to find a feasible solution to a linear equation. Once it is known that either of the problems has a solution by checking the derived conditions, design of control laws is then straightforward. [Copyright &y& Elsevier]

Abstract: This paper proposes a model predictive control (MPC) approach to the periodic implementation of the optimal solutions of a class of resource allocation problems in which the allocation requirements and conditions repeat periodically over time. This special class of resource allocation problems includes many practical energy optimization problems such as load scheduling and generation dispatch. The convergence and robustness of the MPC algorithm is proved by invoking results from convex optimization. To illustrate the practical applications of the MPC algorithm, the energy optimization of a water pumping system is studied. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with the problems of robust and  filtering for 2-dimensional (2-D) discrete-time linear systems described by a Fornasini–Marchesini second model with matrices that depend affinely on convex-bounded uncertain parameters. By a suitable transformation, the system is represented by an equivalent difference-algebraic representation. A parameter-dependent Lyapunov function approach is then proposed for the design of 2-D stationary discrete-time linear filters that ensure either a prescribed performance or  performance for all admissible uncertain parameters. The filter designs are given in terms of linear matrix inequalities. Numerical examples illustrate the effectiveness of the proposed filter design methods. [Copyright &y& Elsevier]