Konstantinos I. Kouramas

Invariant approximations of the minimal robust positively Invariant set

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.

Optimized robust control invariance for linear discrete-time systems: Theoretical foundations

This paper introduces the concept of optimized robust control invariance for discrete-time linear time-invariant systems subject to additive and bounded state disturbances. A novel characterization of two families of robust control invariant sets is given. The existence of a constraint admissible member of these families can be checked by solving a single and tractable convex programming problem in the generic linear-convex case and a standard linear/quadratic program when the constraints are polyhedral or polytopic. The solution of the same optimization problem yields the corresponding feedback control law that is, in general, set-valued. A procedure for selection of a point-valued, nonlinear control law is provided.

MPC on a chip - Recent advances on the application of multi-parametric model-based control

Multi-parametric model-based control (mp-MPC) is a control method that is widely acknowledged for its ability to solve the on-line optimisation problem, involved in traditional MPC, off-line via parametric optimisation. Its main advantage is that it obtains the control actions as explicit functions of the plant measurements. This allows for the control actions to be obtained on-line via simple function evaluations instead of solving repetitively a computationally demanding on-line optimisation. This allows mp-MPC to be implemented on the simplest, low-cost hardware. In this paper we report on recent developments on industrial and experimental applications of mp-MPC, where the ability of mp-MPC to be applied on systems with fast dynamics and sampling times is demonstrated, which maybe prohibitive for traditional MPC that relies on on-line optimisation methods.

On the Minimal Robust Positively Invariant Set for Linear Difference Inclusions

This paper provides a new and efficient method for the computation of an arbitrarily close outer robust positively invariant (RPI) approximation to the minimal robust positively invariant (mRPI) set for linear difference inclusions. It is assumed that the linear difference inclusion is absolutely asymptotically stable (AAS) in the absence of an additive state disturbance, which is the case for parametrically uncertain or switching linear discrete-time systems controlled by a stabilizing linear state feedback controller.

An algorithm for robust explicit/multi-parametric model predictive control

A new algorithm for robust explicit/multi-parametric Model Predictive Control (MPC) for uncertain, linear discrete-time systems is proposed. Based on previous work on Dynamic Programming (DP), multi-parametric Programming and Robust Optimization, the proposed algorithm features, (i) a DP reformulations of the MPC optimization problem, (ii) a robust reformulation of the constraints, and (iii) a multi-parametric programming step, where the control variables are obtained as explicit functions of the state variable, such that the state and input constraints are satisfied for all admissible values of the uncertainty. A key feature of the proposed procedure is that, as opposed to previous methods, it only solves a convex multi-parametric programming problem for each stage of the DP procedure.

Explicit/multi-parametric model predictive control (MPC) of linear discrete-time systems by dynamic and multi-parametric programming

This work presents a new algorithm for solving the explicit/multi-parametric model predictive control (or mp-MPC) problem for linear, time-invariant discrete-time systems, based on dynamic programming and multi-parametric programming techniques. The algorithm features two key steps: (i) a dynamic programming step, in which the mp-MPC problem is decomposed into a set of smaller subproblems in which only the current control, state variables, and constraints are considered, and (ii) a multi-parametric programming step, in which each subproblem is solved as a convex multi-parametric programming problem, to derive the control variables as an explicit function of the states. The key feature of the proposed method is that it overcomes potential limitations of previous methods for solving multi-parametric programming problems with dynamic programming, such as the need for global optimization for each subproblem of the dynamic programming step.

Explicit robust model predictive control

Abstract Abstract Explicit robust multi–parametric feedback control laws are designed for constrained dynamic systems involving uncertainty in the left-hand side(LHS) of the underlying MPC optimization model. Our proposed procedure features: (i) a robust reformulation/optimization step, (ii) a dynamic programming framework for the model predictive control (MPC) problem formulation, and (iii) a multi-parametric programming solution step.

Optimized robust control invariant sets for constrained linear discrete-time systems

Abstract In this paper we introduce the concept of optimized robust control invariance for a discrete-time, linear, time-invariant system subject to additive state disturbances. A novel characterization of a family of the robust control invariant sets is given. The existence of a constraint admissible member of this family can be checked by solving a single linear programming problem. The solution of the same linear programming problem yields the corresponding feedback controller.

Simultaneous design of explicit/multi-parametric constrained moving horizon estimation and robust model predictive control

Abstract In this work we present a rigorous methodology for the simultaneous design of moving horizon estimation (MHE) and robust model predictive control based on multi-parametric programming. First, an explicit/multi-parametric solution of the MHE is derived. Then, a novel method is presented that allows for the derivation of the estimation error dynamics, the bounding set of the estimation error, and the state estimate dynamic equations of constrained MHE. A framework is then presented for the design of robust explicit/multi-parametric model predictive control (MPC) controllers, based on tube-based MPC methods, which ensures that no constraints are violated due to the estimation error and the process noise in the system. This framework is first shown for the Kalman filter and unconstrained MHE and is then extended to the constrained MHE.

Theoretical and algorithmic advances in multi-parametric programming and control

This paper presents an overview of recent theoretical and algorithmic advances, and applications in the areas of multi-parametric programming and explicit/multi-parametric model predictive control (mp-MPC). In multi-parametric programming, advances include areas such as nonlinear multi-parametric programming (mp-NLP), bi-level programming, dynamic programming and global optimization for multi-parametric mixed-integer linear programming problems (mp-MILPs). In multi-parametric/explicit MPC (mp-MPC), advances include areas such as robust multi-parametric control, multi-parametric nonlinear MPC (mp-NMPC) and model reduction in mp-MPC. A comprehensive framework for multi-parametric programming and control is also presented. Recent applications include a hydrogen storage device, a fuel cell power generation system, an unmanned autonomous vehicle (UAV) and a hybrid pressure swing adsorption (PSA) system.