Synthesis of Stabilizing Recurrent Equilibrium Network Controllers

We propose a parameterization of a nonlinear dynamic controller based on the recurrent equilibrium network, a generalization of the recurrent neural network. We derive constraints on the parameterization under which the controller guarantees exponential stability of a partially observed dynamical system with sector-bounded nonlinearities. Finally, we present a method to synthesize this controller using projected policy gradient methods to maximize a reward function with arbitrary structure. The projection step involves the solution of convex optimization problems. We demonstrate the proposed method with simulated examples of controlling nonlinear plants, including plants modeled with neural networks.

Learning Neural Networks under Input-Output Specifications

In this paper, we examine an important problem of learning neural networks that certifiably meet certain specifications on input-output behaviors. Our strategy is to find an inner approximation of the set of admissible policy parameters, which is convex in a transformed space. To this end, we address the key technical challenge of convexifying the verification condition for neural networks, which is derived by abstracting the nonlinear specifications and activation functions with quadratic constraints. In particular, we propose a reparametrization scheme of the original neural network based on loop transformation, which leads to a convex condition that can be enforced during learning. This theoretical construction is validated in an experiment that specifies reachable sets for different regions of inputs.

Recurrent Neural Network Controllers Synthesis with Stability Guarantees for Partially Observed Systems

Neural network controllers have become popular in control tasks thanks to their flexibility and expressivity. Stability is a crucial property for safety-critical dynamical systems, while stabilization of partially observed systems, in many cases, requires controllers to retain and process long-term memories of the past. We consider the important class of recurrent neural networks (RNN) as dynamic controllers for nonlinear uncertain partially-observed systems, and derive convex stability conditions based on integral quadratic constraints, S-lemma and sequential convexification. To ensure stability during the learning and control process, we propose a projected policy gradient method that iteratively enforces the stability conditions in the reparametrized space taking advantage of mild additional information on system dynamics. Numerical experiments show that our method learns stabilizing controllers while using fewer samples and achieving higher final performance compared with policy gradient.

Co-design of Control and Planning for Multi-rotor UAVs with Signal Temporal Logic Specifications

Urban Air Mobility (UAM), or the scenario where multiple manned and Unmanned Aerial Vehicles (UAVs) carry out various tasks over urban airspaces, is a transportation concept of the future that is gaining prominence. UAM missions with complex spatial, temporal and reactive requirements can be succinctly represented using Signal Temporal Logic (STL), a behavioral specification language. However, planning and control of systems with STL specifications is computationally intensive, usually resulting in planning approaches that do not guarantee dynamical feasibility, or control approaches that cannot handle complex STL specifications. Here, we present an approach to co-design the planner and control such that a given STL specification (possibly over multiple UAVs) is satisfied with trajectories that are dynamically feasible and our controller can track them with a bounded tracking-error that the planner accounts for. The tracking controller is formulated for the non-linear dynamics of the individual UAVs, and the tracking error bound is computed for this controller when the trajectories satisfy some kinematic constraints. We also augment an existing multi-UAV STL-based trajectory generator in order to generate trajectories that satisfy such constraints. We show that this co-design allows for trajectories that satisfy a given STL specification, and are also dynamically feasible in the sense that they can be tracked with bounded error. The applicability of this approach is demonstrated through simulations of multi-UAV missions.