Time-variant receding-horizon control of nonlinear systems

The conventional real-time optimization algorithm is extended to the receding-horizon state feedback control problem with time-invariant parameters. An algorithm is derived in a modified manner and showed that the unknown costate, governed by a differential equation, is a natural extension of the Euler-Lagrange equations for a finite horizon optimal control problem with fixed terminal time. It results in less computation and data storage than a direct extension of the conventional algorithm. A tracking control problem of a two-wheeled car is employed as a numerical example. Simulation demonstrates that the receding-horizon tracking control achieves the best performance even if the reference trajectory cannot be tracked perfectly with any control unit.