Rien Quirynen

Pedro Hespanhol, Rien Quirynen, Stefano Di Cairano

Mixed-integer model predictive control (MI-MPC) requires the solution of a mixed-integer quadratic program (MIQP) at each sampling instant under strict timing constraints, where part of the state and control variables can only assume a discrete set of values. Several applications in automotive, aerospace and hybrid systems are practical examples of how such discrete-valued variables arise. We utilize the sequential nature and the problem structure of MI-MPC in order to provide a branch-and-bound algorithm that can exploit not only the block-sparse optimal control structure of the problem but that can also be warm started by propagating information from branch-and-bound trees and solution paths at previous time steps. We illustrate the computational performance of the proposed algorithm and compare against current state-of-the-art solvers for multiple MPC case studies, based on a preliminary implementation in MATLAB and C code.

Sleiman Safaoui, Abraham P. Vinod, Ankush Chakrabarty et al.

We consider the problem of safe multi-agent motion planning for drones in uncertain, cluttered workspaces. For this problem, we present a tractable motion planner that builds upon the strengths of reinforcement learning and constrained-control-based trajectory planning. First, we use single-agent reinforcement learning to learn motion plans from data that reach the target but may not be collision-free. Next, we use a convex optimization, chance constraints, and set-based methods for constrained control to ensure safety, despite the uncertainty in the workspace, agent motion, and sensing. The proposed approach can handle state and control constraints on the agents, and enforce collision avoidance among themselves and with static obstacles in the workspace with high probability. The proposed approach yields a safe, real-time implementable, multi-agent motion planner that is simpler to train than methods based solely on learning. Numerical simulations and experiments show the efficacy of the approach.

Pedro Hespanhol, Rien Quirynen

Nonlinear model predictive control~(NMPC) generally requires the solution of a non-convex optimization problem at each sampling instant under strict timing constraints, based on a set of differential equations that can often be stiff and/or that may include implicit algebraic equations. This paper provides a local convergence analysis for the recently proposed adjoint-based sequential quadratic programming~(SQP) algorithm that is based on a block-structured variant of the two-sided rank-one~(TR1) quasi-Newton update formula to efficiently compute Jacobian matrix approximations in a sparsity preserving fashion. A particularly efficient algorithm implementation is proposed in case an implicit integration scheme is used for discretization of the optimal control problem, in which matrix factorization and matrix-matrix operations can be avoided entirely. The convergence analysis results as well as the computational performance of the proposed optimization algorithm are illustrated for two simulation case studies of nonlinear MPC.

Ankush Chakrabarty, Rien Quirynen, Claus Danielson et al.

Enforcing state and input constraints during reinforcement learning (RL) in continuous state spaces is an open but crucial problem which remains a roadblock to using RL in safety-critical applications. This paper leverages invariant sets to update control policies within an approximate dynamic programming (ADP) framework that guarantees constraint satisfaction for all time and converges to the optimal policy (in a linear quadratic regulator sense) asymptotically. An algorithm for implementing the proposed constrained ADP approach in a data-driven manner is provided. The potential of this formalism is demonstrated via numerical examples.