This paper is concerned with the optimal control of linear discrete-time systems subject to unknown but bounded state disturbances and mixed polytopic constraints on the state and input. It is shown that the class of admissible affine state feedback control policies with knowledge of prior states is equivalent to the class of admissible feedback policies that are affine functions of the past disturbance sequence. This implies that a broad class of constrained finite horizon robust and optimal control problems, where the optimization is over affine state feedback policies, can be solved in a computationally efficient fashion using convex optimization methods. This equivalence result is used to design a robust receding horizon control (RHC) state feedback policy such that the closed-loop system is input-to-state stable (ISS) and the constraints are satisfied for all time and all allowable disturbance sequences. The cost to be minimized in the associated finite horizon optimal control problem is quadratic in the disturbance-free state and input sequences. The value of the receding horizon control law can be calculated at each sample instant using a single, tractable and convex quadratic program (QP) if the disturbance set is polytopic, or a tractable second-order cone program (SOCP) if the disturbance set is given by a 2-norm bound.

performs better than the already classical balanced truncation method even when its static matrix gain is optimized, procedure which involves greater computational efforts. Our method performs particularly well when approximations of large scale flexible structures are considered and we believe that it is a real alternative to determine reduced order models of this important class of linear time invariant systems. [3] Y. Ebihara and T. Hagiwara, "On H model reduction using LMIs," REFERENCESIEEE Trans. Autom. Control, vol. 49, no. 7, pp. 1187-1191 J. C. Geromel, "Convex analysis and global optimization of joint actuator location and control problems," IEEE Trans. Autom. Control, vol. 34, no. 7, pp. 711-720, Jul. 1989. [5] , "Optimal linear filtering under parameter uncertainty," IEEE Trans. Signal Process., vol. 47, no. 1, pp. 168-175, Jan. 1999. [6] J. C. Geromel, F. R. R. Kawaoka, and R. G. Egas, "Model reduction of discrete time systems through linear matrix inequalities," Int. J. Control, vol. 77, no. 10, pp. 978-984, Jul. 2004. [7] K. Glover, "All optimal Hankel-norm approximations of linear multivariable systems and their L -error bounds," Int. J. Control, vol. 39, no. 6, pp. 1115Control, vol. 39, no. 6, pp. -1193Control, vol. 39, no. 6, pp. , 1984 [8] K. M. Grigoriadis, "Optimal H model reduction via linear matrix inequalities: Continuous and discrete-time cases," Syst. Control Lett., vol. 26, no. 5, pp. 321-333, 1995. [9] W. M. Haddad and D. S. Bernstein, "Combined L =H model-reduction," Int. J. Control, vol. 49, no. 5, pp. 1523Control, vol. 49, no. 5, pp. -1535Control, vol. 49, no. 5, pp. , 1989 [10] L. Meirovitch, H. Baruh, and H. Öz, "A comparison of control techniques for large flexible systems," J. Guid., vol. 6, no. 4, 1983. [11] C. Scherer, "Mixed H =H Abstract-This note provides results on approximating the minimal robust positively invariant (mRPI) set (also known as the 0-reachable set) of an asymptotically stable discrete-time linear time-invariant system. It is assumed that the disturbance is bounded, persistent and acts additively on the state and that the constraints on the disturbance are polyhedral. Results are given that allow for the computation of a robust positively invariant, outer approximation of the mRPI set. Conditions are also given that allow one to a priori specify the accuracy of this approximation.

SUMMARYThis paper extends tube-based model predictive control of linear systems to achieve robust control of nonlinear systems subject to additive disturbances. A central or reference trajectory is determined by solving a nominal optimal control problem. The local linear controller, employed in tube-based robust control of linear systems, is replaced by an ancillary model predictive controller that forces the trajectories of the disturbed system to lie in a tube whose center is the reference trajectory thereby enabling robust control of uncertain nonlinear systems to be achieved.

Faster, cheaper, and more power efficient optimization solvers than those currently possible using general-purpose techniques are required for extending the use of model predictive control (MPC) to resource-constrained embedded platforms. We propose several custom computational architectures for different first-order optimization methods that can handle linear-quadratic MPC problems with input, input-rate, and soft state constraints. We provide analysis ensuring the reliable operation of the resulting controller under reduced precision fixed-point arithmetic. Implementation of the proposed architectures in FPGAs shows that satisfactory control performance at a sample rate beyond 1 MHz is achievable even on low-end devices, opening up new possibilities for the application of MPC on embedded systems.Index Terms-Embedded systems, optimization algorithms, predictive control of linear systems.

SUMMARYIn this paper we introduce a new stage cost and show that the use of this cost allows one to formulate a robustly stable feedback min-max model predictive control problem that can be solved using a single linear program. Furthermore, this is a multi-parametric linear program, which implies that the optimal control law is piecewise affine, and can be explicitly pre-computed so that the linear program does not have to be solved on-line. We assume that the plant model is known, is discrete-time and linear time-invariant, is subject to unknown but bounded state disturbances and that the states of the system are measured. Two numerical examples are presented; one of these is taken from the literature, so that a direct comparison of solutions and computational complexity with earlier proposals is possible. This is a preprint of an article published in International Journal of Robust and Nonlinear Control