Claus Danielson

Claus Danielson, Avishai Weiss, Karl Berntorp et al.

We present an algorithm for steering the output of a linear system from a feasible initial condition to a desired target position, while satisfying input constraints and non-convex output constraints. The system input is generated by a collection of local linear state-feedback controllers. The path-planning algorithm selects the appropriate local controller using a graph search, where the nodes of the graph are the local controllers and the edges of the graph indicate when it is possible to transition from one local controller to another without violating input or output constraints. We present two methods for computing the local controllers. The first uses a fixed-gain controller and scales its positive invariant set to satisfy the input and output constraints. We provide a linear program for determining the scale-factor and a condition for when the linear program has a closed-form solution. The second method designs the local controllers using a semi-definite program that maximizes the volume of the positive invariant set that satisfies state and input constraints. We demonstrate our path-planning algorithm on docking of a spacecraft. The semi-definite programming based control design has better performance but requires more computation.

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.