Iterative Model Predictive Control for Piecewise Systems

Abstract

In this paper, we present an iterative Model Predictive Control (MPC) design for piecewise nonlinear systems. We consider finite time control tasks where the goal of the controller is to steer the system from a starting configuration to a goal state while minimizing a cost function. First, we present an algorithm that leverages a feasible trajectory that completes the task to construct a control policy which guarantees that state and input constraints are recursively satisfied and that the closed-loop system reaches the goal state in finite time. Utilizing this construction, we present a policy iteration scheme that iteratively generates safe trajectories which have nondecreasing performance. Finally, we test the proposed strategy on a discretized Spring Loaded Inverted Pendulum (SLIP) model with massless legs. We show that our methodology is robust to changes in initial conditions and disturbances acting on the system. Furthermore, we demonstrate the effectiveness of our policy iteration algorithm in a minimum time control task.

Online Target Localization Using Adaptive Belief Propagation in the HMM Framework

“…Additionally, it seamlessly incorporates geometric information, such as barriers or boundaries, into localization [21]. Furthermore, integration with the control and planning pipeline is readily achieved, as finite state-based techniques commonly establish action (control) policies [22], [23]. represents a multivariate random variable (random vector) at every time step.…”