Finite Horizon Backward Reachability Analysis and Control Synthesis for Uncertain Nonlinear Systems
This work provides a computationally tractable approach for finite-horizon reachability and control of uncertain nonlinear systems, which is important for safety-critical applications.
The paper presents a method for synthesizing controllers to steer trajectories from an initial set to a target set within a finite horizon, using storage functions to under-approximate backward reachable sets and a min-norm optimization for control law. The method is extended to uncertain nonlinear systems and demonstrated on robotics and aircraft examples.
We present a method for synthesizing controllers to steer trajectories from an initial set to a target set on a finite time horizon. The proposed control synthesis problem is decomposed into two steps. The first step under-approximates the backward reachable set (BRS) from the target set, using level sets of storage functions. The storage function is constructed with an iterative algorithm to maximize the volume of the under-approximated BRS. The second step obtains a control law by solving a pointwise min-norm optimization problem using the pre-computed storage function. A closed-form solution of this min-norm optimization can be computed through the KKT conditions. This control synthesis framework is then extended to uncertain nonlinear systems with parametric uncertainties and L_2 disturbances. The computation algorithm for all cases is derived using sum-of-squares (SOS) programming and the S-procedure. The proposed method is applied to several robotics and aircraft examples.