Stability and Incremental Improvement of Suboptimal MPC Without Terminal Constraints

• Published in: IEEE transactions on automatic control Vol. 55; no. 11; pp. 2576 - 2580
• Main Authors: Graichen, K, Kugi, A
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.11.2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Asymptotic stability; Automatic control; Computer science; control theory; systems; Control Lyapunov function (CLF); Control system analysis; Control theory. Systems; Convergence; Cost function; Decay; Dynamical systems; Errors; Exact sciences and technology; Iterative methods; model predictive control (MPC); Nonlinear systems; Optimal control; optimal control problem (OCP); Optimization; Predictive control; Predictive models; Sampling; Sampling methods; Stability; Terminal constraints; Lower bound; Suboptimal control; Control system analysis; Control Lyapunov function (CLF); Non linear control; Continuous time; optimal control problem (OCP); Dynamical system; Exponential stability; Non linear system; Optimization; model predictive control (MPC); Model predictive control; Optimal control; Sampling; Lyapunov function
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2010.2057912

The stability of suboptimal model predictive control (MPC) without terminal constraints is investigated for continuous-time nonlinear systems under input constraints. Exponential stability and decay of the optimization error are guaranteed if the number of optimization steps in each sampling instant satisfies a lower bound that depends on the convergence ratio of the underlying optimization algorithm. The decay of the optimization error shows the incremental improvement of the suboptimal MPC scheme.