A Hierarchical MPC Approach with Guaranteed Feasibility for Dynamically Coupled Linear Systems

In this chapter we describe an iterative two-layer hierarchical approach to MPC of large-scale linear systems subject to coupled linear constraints. The algorithm uses constraint tightening and applies a primal-dual iterative averaging procedure to provid

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A Hierarchical MPC Approach with Guaranteed Feasibility for Dynamically Coupled Linear Systems M. D. Doan, T. Keviczky and B. De Schutter

Abstract In this chapter we describe an iterative two-layer hierarchical approach to MPC of large-scale linear systems subject to coupled linear constraints. The algorithm uses constraint tightening and applies a primal-dual iterative averaging procedure to provide feasible solutions in every sampling step. This helps overcome typical practical issues related to the asymptotic convergence of dual decomposition based distributed MPC approaches. Bounds on constraint violation and level of suboptimality are provided. The method can be applied to large-scale MPC problems that are feasible in the first sampling step and for which the Slater condition holds (i.e., there exists a solution that strictly satisfies the inequality constraints). Using this method, the controller can generate feasible solutions of the MPC problem even when the dual solution does not reach optimality, and closed-loop stability is also ensured using bounded suboptimality.

24.1 Introduction When there are couplings among linear subsystems in a distributed MPC problem, dual decomposition is often used in order to divide the computational tasks among the subsystems. A typical requirement of the dual decomposition-based methods is that the dual problem needs to be solved exactly in order to obtain a primal M. D. Doan · T. Keviczky (B) · B. Schutter Delft Center for Systems and Control, Delft University of Technology, Delft, The Netherlands e-mail: [email protected] M. D. Doan e-mail: [email protected] T. Keviczky e-mail: [email protected] B. Schutter e-mail: [email protected] J. M. Maestre and R. R. Negenborn (eds.), Distributed Model Predictive Control 393 Made Easy, Intelligent Systems, Control and Automation: Science and Engineering 69, DOI: 10.1007/978-94-007-7006-5_24, © Springer Science+Business Media Dordrecht 2014

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feasible solution [1]. However, iterative approaches based on dual decomposition often only converge asymptotically to the optimum, which may not be practical when implementing these approaches in a real-time environment. In this chapter, we apply a dual decomposition technique to the class of MPC problems for linear systems with coupled dynamics and coupled linear constraints, and propose a novel method that is motivated by the use of constraint tightening in robust MPC [5]. This method allows terminating the iterations for the dual problem before reaching convergence while still guaranteeing a feasible primal solution to be found. Moreover, the algorithm also generates a decreasing cost function, leading to closed-loop stability. In summary, the proposed framework guarantees primal feasible solutions and MPC stability using a finite number of iterations with bounded suboptimality.

24.2 Boundary Conditions Our approach aims at large-scale interconnected systems with constrained discretetime linear time-invariant dynamics where some of the individual co