Receding-Horizon Nonlinear Optimal Control With Safety Constraints Using Constrained Approximate Dynamic Programming

Abstract

We present a receding-horizon optimal control for nonlinear continuous-time systems subject to state constraints. The cost is a quadratic finite-horizon integral. The key enabling technique is a new constrained approximate dynamic programming (C-ADP) approach for finite-horizon nonlinear optimal control with constraints that are affine in the control. The C-ADP approach is intuitive because it uses a quadratic approximation of the cost-to-go function at each backward step. This method yields a sequence of analytic closed-form optimal control functions, which have identical structure and where parameters are obtained from 2 Riccati-like difference equations. This C-ADP method is well suited for real-time implementation. Thus, we use the C-ADP approach in combination with control barrier functions to obtain a continuous-time receding-horizon optimal control that is farsighted in the sense that it optimizes the integral cost subject to state constraints along the entire prediction horizon. Lastly, receding-horizon C-ADP control is demonstrated in simulation of a nonholonomic ground robot subject to velocity and no-collision constraints. We compare performance with 3 other approaches.

Figures (2)

• Figure D1: All 15 trajectories for each method. Blue lines indicate trajectories that reach $q_{\rm d}$, whereas red lines do not.
• Figure D2: Performance and control metrics. Red lines show the mean, and the dashed lines show the 15 trials.

Theorems & Definitions (1)

• proof : Proof