81,691 research outputs found
Robust Differentiable Predictive Control with Safety Guarantees: A Predictive Safety Filter Approach
In this paper, we propose a novel predictive safety filter that is robust to
bounded perturbations and is combined with a learning-based control called
differentiable predictive control (DPC). The proposed method provides rigorous
guarantees of safety in the presence of bounded perturbations and implements
DPC so long as the DPC control satisfies the system constraints. The approach
also incorporates two forms of event-triggering to reduce online computation.
The approach is comprised of a robust predictive safety filter that extends
upon existing work to reject disturbances for discrete-time, time-varying
nonlinear systems with time-varying constraints. The safety filter is based on
novel concepts of robust, discrete-time barrier functions and can be used to
filter any control law. Here we use the safety filter in conjunction with DPC
as a promising policy optimization method. The approach is demonstrated on a
single-integrator, two-tank system, and building example.Comment: Submitted to Automatic
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Optimization-Based Drift Prevention for Learning Control of Underdetermined Linear and Weakly Nonlinear Time-Varying Systems
In this paper an optimization-based method of drift prevention is presented for learning control of underdetermined linear and weakly nonlinear time-varying dynamic systems. By defining a fictitious cost function and the associated model-based sub-optimality conditions, a new set of equations results, whose solution is unique, thus preventing large drifts from the initial input. Moreover, in the limiting case where the modeling error approaches zero, the input that the proposed method converges to is the unique feasible (zero error) input that minimizes the fictitious cost function, in the linear case, and locally minimizes it in the (weakly) nonlinear case. Otherwise, under mild restrictions on the modeling error, the method converges to a feasible sub-optimal input
Learning-based Predictive Control for Nonlinear Systems with Unknown Dynamics Subject to Safety Constraints
Model predictive control (MPC) has been widely employed as an effective
method for model-based constrained control. For systems with unknown dynamics,
reinforcement learning (RL) and adaptive dynamic programming (ADP) have
received notable attention to solve the adaptive optimal control problems.
Recently, works on the use of RL in the framework of MPC have emerged, which
can enhance the ability of MPC for data-driven control. However, the safety
under state constraints and the closed-loop robustness are difficult to be
verified due to approximation errors of RL with function approximation
structures. Aiming at the above problem, we propose a data-driven robust MPC
solution based on incremental RL, called data-driven robust learning-based
predictive control (dr-LPC), for perturbed unknown nonlinear systems subject to
safety constraints. A data-driven robust MPC (dr-MPC) is firstly formulated
with a learned predictor. The incremental Dual Heuristic Programming (DHP)
algorithm using an actor-critic architecture is then utilized to solve the
online optimization problem of dr-MPC. In each prediction horizon, the actor
and critic learn time-varying laws for approximating the optimal control policy
and costate respectively, which is different from classical MPCs. The state and
control constraints are enforced in the learning process via building a
Hamilton-Jacobi-Bellman (HJB) equation and a regularized actor-critic learning
structure using logarithmic barrier functions. The closed-loop robustness and
safety of the dr-LPC are proven under function approximation errors. Simulation
results on two control examples have been reported, which show that the dr-LPC
can outperform the DHP and dr-MPC in terms of state regulation, and its average
computational time is much smaller than that with the dr-MPC in both examples.Comment: The paper has been submitted at a IEEE Journal for possible
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