Dewei Li

Technical communique: An improved robust model predictive control design in the presence of actuator saturation

A new robust model predictive control (RMPC) design algorithm is proposed for a linear uncertain system with a polytopic description and subject to actuator saturation. This algorithm involves the solution of an infinite horizon LQR problem for the uncertain system in the presence of actuator saturation at each time instant and the implementation of the first element of the resulting optimal control profile. By expressing a saturating linear feedback law on a convex hull of a group of auxiliary linear feedback laws and the actual linear feedback law, the LQR problem can be solved for a group of linear polytopic systems in the absence of saturation, with heavier weighting placed on the system corresponding to the actual linear feedback law. The additional design freedom in choosing the relative weighting on the actual and auxiliary feedback laws allows further improvement of the closed-loop system performance over those resulting from the existing algorithms. A numerical example illustrates the effectiveness of the proposed algorithm.

Synthesis of dynamic output feedback RMPC with saturated inputs

For polytopic uncertain systems with unmeasurable system states, a synthesis of output feedback robust model predictive control (OFRMPC) is proposed, which adopts a category of dynamic output feedback controller. In order to improve the utilization of the actuator capability, the saturation function is applied to the output of the dynamic output feedback controller. Based on it, the OFRMPC is proposed with an online update algorithm of the estimated error set. All the designs are verified to considerably improve the control performance. Meanwhile, a simplified design of OFRMPC is also developed to make the proposed design more practical.

The Feedback Robust MPC for LPV Systems With Bounded Rates of Parameter Changes

This note addresses the feedback robust model predictive control (FRMPC) for a category of linear parameter varying (LPV) systems with bounded rates of parameter changes. Based on the bounded rates of parameter changes and the detected current system parameters, future model variations can be described by a sequence of polytopic families with the same number of vertices. Then a FRMPC algorithm is developed. Since both the future model variations and the corresponding sequence of feedback control laws are adopted, the FRMPC can achieve high control performance. By transferring main design work to offline design, an efficient FRMPC is also developed. The recursive feasibility and closed-loop stability of the FRMPCs are proved to be guaranteed.

Constrained robust feedback model predictive control for uncertain systems with polytopic description

For the constrained uncertain systems with polytopic description, a new design method of robust feedback model predictive control is proposed. By using a sequence of feedback control laws and designing the parameter-dependent Lyapunov function for each model, the design method provides more degrees of freedom and then can improve the control performance and enlarge the feasible region. Based on the characteristic property of the design method, an offline design algorithm is developed to reduce the MPC controllers online computation burden. The numerical examples verify the effectiveness of the results presented in this article.

Constrained predictive control synthesis for quantized systems with Markovian data loss

This paper investigates the predictive control synthesis problem for constrained feedback control systems with both missing data and quantization. By introducing a missing data compensation strategy and an augmented Markov jump linear model with polytopic uncertainties, the effects of data loss and quantization on the system performance are considered simultaneously. A robust predictive control synthesis approach involving data missing and recovering probabilities is developed by minimizing an upper bound on the expected value of an infinite horizon quadratic performance objective at each sampling instant. Additional conditions to satisfy the input constraint in the presence of multiple missing data are also incorporated into the model predictive control (MPC) synthesis. Furthermore, both the recursive feasibility of the proposed MPC algorithm and the closed-loop mean-square stability are proved. Simulation results are given to illustrate the effectiveness of the proposed approach.

Constrained feedback robust model predictive control for polytopic uncertain systems with time delays

An approach to design robust model predictive control (MPC) is proposed by considering constrained time-delayed systems with polytopic uncertainty description. The contribution consists of two aspects. First, compared with the existing techniques which apply a single state feedback law, the feedback MPC is utilised, which applies a sequence of feedback control laws. Second, for systems with input delay, an augmented polytopic uncertainty description is invoked to remove the input delay. By feedback MPC, the conservativeness of the traditional MPC is reduced. By the augmented system description, the difficulties in handling the input delay, such as inability to deal with some unstable system matrices in the previous robust MPC literature, are overcome. Two simulation results are given to illustrate the effectiveness of the proposed approach.

Probability-based constrained MPC for structured uncertain systems with state and random input delays

This article is concerned with probability-based constrained model predictive control (MPC) for systems with both structured uncertainties and time delays, where a random input delay and multiple fixed state delays are included. The process of input delay is governed by a discrete-time finite-state Markov chain. By invoking an appropriate augmented state, the system is transformed into a standard structured uncertain time-delay Markov jump linear system (MJLS). For the resulting system, a multi-step feedback control law is utilised to minimise an upper bound on the expected value of performance objective. The proposed design has been proved to stabilise the closed-loop system in the mean square sense and to guarantee constraints on control inputs and system states. Finally, a numerical example is given to illustrate the proposed results.

The synthesis of robust model predictive control with QP formulation

For uncertain systems with polytopic description, two synthesis approaches of closed-loop robust model predictive control (CRMPC) are proposed. The proposed CRMPC controllers are formulated as a quadratic programming (QP) problem to reduce the online computational burden. By adopting the dual-mode control and extending the interpolation method, the time-varying terminal set is introduced into CRMPC with QP formulation. Meanwhile, the tighter upper bound of control performance is utilised. Due to these two factors, the proposed CRMPC can achieve large attractive region and improved control performance with low online computational burden.

Quality guaranteed aggregation based model predictive control and stability analysis

The input aggregation strategy can reduce the online computational burden of the model predictive controller. But generally aggregation based MPC controller may lead to poor control quality. Therefore, a new concept, equivalent aggregation, is proposed to guarantee the control quality of aggregation based MPC. From the general framework of input linear aggregation, the design methods of equivalent aggregation are developed for unconstrained and terminal zero constrained MPC, which guarantee the actual control inputs exactly to be equal to that of the original MPC. For constrained MPC, quasi-equivalent aggregation strategies are also discussed, aiming to make the difference between the control inputs of aggregation based MPC and original MPC as small as possible. The stability conditions are given for the quasi-equivalent aggregation based MPC as well.

Mixed H2/H∞ robust model predictive control with saturated inputs

In this paper, we investigate the mixed H2/H∞ robust model predictive control (RMPC) for polytopic uncertain systems, which refers to the infinite horizon optimal guaranteed cost control (OGCC). To fully use the capability of actuators, we adopt a saturating feedback control law as the control strategy of RMPC. As the saturating feedback control law can be effectively represented by the convex hull of a group of auxiliary linear feedback laws, the auxiliary feedback laws allow us to design the actual feedback control law without consideration of the input constraints directly to achieve the improved performance. Moreover, we suggest the relative weights on the actual and auxiliary feedback laws to the RMPC, which in turn improves the closed-loop system performance. Furthermore, an off-line design of the proposed RMPC is also developed to make it more practical. Numerical studies demonstrate the effectiveness of the proposed algorithm.