Distributed Lyapunov-Based MPC
We provide an almost decentralized solution to the problem of stabilizing a network of discrete-time nonlinear systems with coupled dynamics that are subject to local state/input constraints. By “almost decentralized” we mean that each local controller is
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Distributed Lyapunov-Based MPC R. Hermans, M. Lazar and A. Joki´c
Abstract We provide an almost decentralized solution to the problem of stabilizing a network of discrete-time nonlinear systems with coupled dynamics that are subject to local state/input constraints. By “almost decentralized” we mean that each local controller is allowed to use the states of neighboring systems for feedback, whereas it is not permitted to employ iterations between the systems in the network to compute the control action. The controller synthesis method used in this work is Lyapunov-based model predictive control. The closed-loop stability conditions are decentralized via a set of structured control Lyapunov functions (CLFs) for which the maximum over all the functions in the set is a CLF for the global network of systems. However, this does not necessarily imply that each function is a CLF for its corresponding subsystem. Additionally, a solution is provided for relaxing the temporal monotonicity of the network-wide CLF. For infinity-norm based structured CLFs and input-affine dynamics, we show that the decentralized MPC algorithm can be implemented by solving a single linear program in each network node. Two application examples are provided to illustrate the effectiveness of the developed theory and to show that the proposed method can perform as well as more complex distributed, iteration-based MPC algorithms.
R. Hermans (B) · M. Lazar Department of Electrical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands e-mail: [email protected] M. Lazar e-mail: [email protected] A. Joki´c Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb, Croatia e-mail: [email protected]
J. M. Maestre and R. R. Negenborn (eds.), Distributed Model Predictive Control 225 Made Easy, Intelligent Systems, Control and Automation: Science and Engineering 69, DOI: 10.1007/978-94-007-7006-5_14, © Springer Science+Business Media Dordrecht 2014
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14.1 Introduction The basic requirement of any control system is that the corresponding closed-loop dynamics are stable. In standard model predictive control schemes, this is typically guaranteed via monotonic convergence of the subsequent optimal performance cost values, see, e.g., [11]. Hence, in these cost-based approaches, attaining globally optimal performance is a key prerequisite for stability. Unfortunately, when non-centralized MPC for large-scale networks of interconnected dynamical systems (NDS) is the main focus, the demand for optimization of a system-wide performance cost function inherently comes with a need for intensive iterative exchange of information or global coordination among the agents that control the various subsystems in the network. Such coordination may be hampered by limitations of the communication infrastructure that is available in practice, or may be undesired in competitive environments such as the deregulated electrical power market [3]. A successful alternative to cost based stabilization is Lyapuno
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