Distributed stochastic MPC for systems with parameter uncertainty and disturbances

Abstract

Summary A distributed stochastic model predictive control algorithm is proposed for multiple linear subsystems with both parameter uncertainty and stochastic disturbances, which are coupled via probabilistic constraints. To handle the probabilistic constraints, the system dynamics is first decomposed into a nominal part and an uncertain part. The uncertain part is further divided into 2 parts: the first one is constrained to lie in probabilistic tubes that are calculated offline through the use of the probabilistic information on disturbances, whereas the second one is constrained to lie in polytopic tubes whose volumes are optimized online and whose facets' orientations are determined offline. By permitting a single subsystem to optimize at each time step, the probabilistic constraints are then reduced into a set of linear deterministic constraints, and the online optimization problem is transformed into a convex optimization problem that can be performed efficiently. Furthermore, compared to a centralized control scheme, the distributed stochastic model predictive control algorithm only requires message transmissions when a subsystem is optimized, thereby offering greater flexibility in communication. By designing a tailored invariant terminal set for each subsystem, the proposed algorithm can achieve recursive feasibility, which, in turn, ensures closed‐loop stability of the entire system. A numerical example is given to illustrate the efficacy of the algorithm.

Robust model predictive control for polytopic uncertain systems with state saturation nonlinearities under Round‐Robin protocol

“…By selecting the same sampling period as in the work of Al-Gherwi et al, 18 the corresponding discrete-time system can be readily obtained. In addition, parameter uncertainties are considered into system matrices for the practical view point, thus matrix vertices A (1) and A (2) are derived as follows:…”

“…In the past few decades, model predictive control (MPC), known as receding horizon control, has received particular research attention because of its great potential in handling the optimization problems including input, state/output constraints. So far, an MPC strategy has been extensively applied into various industries and a rich body of the results has been reported in the literature . Note that the aforementioned MPC strategies for nominal systems might be invalid for systems with parameter uncertainties.…”

“…So far, an MPC strategy has been extensively applied into various industries and a rich body of the results has been reported in the literature. [1][2][3][4][5] Note that the aforementioned MPC strategies [6][7][8][9] for nominal systems might be invalid for systems with parameter uncertainties. It is, therefore, vitally important to develop some new MPC strategies to guarantee the system robustness against the parameter uncertainties, which readily gives rise to the robust MPC (RMPC).…”

Event‐triggered model predictive control for multi‐vehicle systems with collision avoidance and obstacle avoidance

“…10 By solving a finite predictive horizon open-loop optimal control problem, a current control action is obtained online at each sample instant using the MPC strategy. 11,12 An MPC strategy is proposed to solve a constrained tracking problem for a linear system with bounded disturbances under infeasible references. 13 For tracking and formation of multi-vehicle systems, a synchronous distributed MPC strategy is presented in Reference 14.…”

A Novel Fuzzy Model Predictive Control of a Gas Turbine in the Combined Cycle Unit

“…Although this method showed better properties with ideal tracking performance and strong disturbance rejection ability, the accompanying increased calculation burden was ignored at the same time. Furthermore, the distributed stochastic MPC [31,32] was adopted for these control systems with uncertainty and probabilistic constraints as well as disturbances. According to the distribution manner, only one subsystem was selected at each time interval.…”