Reduced-complexity interpolating control of constrained interconnected systems and applications

Nowadays control research focuses on the constrained control of large-scale systems. Controlling a large-scale system in a centralised way can be computationally expensive. Thus, there is a need to develop efficient control strategies for embedded real-time control. Large-scale systems can be decomposed into a number of interconnected subsystems where each local controller regulates a single region. To investigate reduced-complexity control schemes, this work adopts and extends the interpolating control (IC) approach. IC offers an enlarged stabilising region and inexpensive online computations. The main idea of IC is to blend a local high-gain controller, which satisfy some user-desired performance, with a global low-gain controller via convex interpolation. The first part of the thesis develops a reduced-complexity interpolating control scheme (dIC) for the decentralised control of interconnected systems with well-structured decoupled information constraints. The key idea is to solve constrained control problems via distributed interpolation in low-dimensional topologies. To implement this, computation of separable invariant sets for each subsystem is carried out. For the synthesis of the controller, a low-dimensional linear programming problem (LP) is solved at each time step. For systems characterised by polytopic uncertainty robust decentralised interpolating control is presented as extension of dIC. Proofs of recursive feasibility and asymptotic stability are given. Results demonstrate that the proposed (robust) interpolating control guarantees feasibility and stability of the overall system with low computational requirements compared to centralised interpolating control. The second part of the thesis proposes that different invariant sets that can be used to enlarge the stabilising region in case that (robust) controllable invariant sets cannot be determined or are unknown during the design process. They provide a fair representation of controllable invariant sets and low complexity, and thus can be used to develop innovative interpolating control schemes. This interpolating control formulation calls for the solution of an inexpensive LP problem, while its complexity depends on the size of the problem that can be alleviated by a distributed formulation. Results demonstrate that the reduced-complexity decentralised formulation provides an outstanding reduction of the required computation effort compared to standard decentralised interpolating control. The third part of this thesis demonstrates the effectiveness of the proposed constrained interpolating control to solve a number of real world applications concerning interconnected linear time-invariant and time-varying systems