Scalable Robust Adaptive Control from the System Level Perspective

We will present a new general framework for robust and adaptive control that allows for distributed and scalable learning and control of large systems of interconnected linear subsystems. The control method is demonstrated for a linear time-invariant system with bounded parameter uncertainties, disturbances and noise. The presented scheme continuously collects measurements to reduce the uncertainty about the system parameters and adapts dynamic robust controllers online in a stable and performance-improving way. A key enabler for our approach is choosing a time-varying dynamic controller implementation, inspired by recent work on System Level Synthesis [1]. We leverage a new robustness result for this implementation to propose a general robust adaptive control algorithm. In particular, the algorithm allows us to impose communication and delay constraints on the controller implementation and is formulated as a sequence of robust optimization problems that can be solved in a distributed manner. The proposed control methodology performs particularly well when the interconnection between systems is sparse and the dynamics of local regions of subsystems depend only on a small number of parameters. As we will show on a five-dimensional exemplary chain-system, the algorithm can utilize system structure to efficiently learn and control the entire system while respecting communication and implementation constraints. Moreover, although current theoretical results require the assumption of small initial uncertainties to guarantee robustness, we will present simulations that show good closed-loop performance even in the case of large uncertainties, which suggests that this assumption is not critical for the presented technique and future work will focus on providing less conservative guarantees

Separating Controller Design from Closed-Loop Design: A New Perspective on System-Level Controller Synthesis

We show that given a desired closed-loop response for a system, there exists an affine subspace of controllers that achieve this response. By leveraging the existence of this subspace, we are able to separate controller design from closed-loop design by first synthesizing the desired closed-loop response and then synthesizing a controller that achieves the desired response. This is a useful extension to the recently introduced System Level Synthesis framework, in which the controller and closed-loop response are jointly synthesized and we cannot enforce controller-specific constraints without subjecting the closed-loop map to the same constraints.We demonstrate the importance of separating controller design from closed-loop design with an example in which communication delay and locality constraints cause standard SLS to be infeasible. Using our new two-step procedure, we are able to synthesize a controller that obeys the constraints while only incurring a 3% increase in LQR cost compared to the optimal LQR controller

Separating Controller Design from Closed-Loop Design: A New Perspective on System-Level Controller Synthesis

We show that given a desired closed-loop response for a system, there exists an affine subspace of controllers that achieve this response. By leveraging the existence of this subspace, we are able to separate controller design from closed-loop design by first synthesizing the desired closed-loop response and then synthesizing a controller that achieves the desired response. This is a useful extension to the recently introduced System Level Synthesis framework, in which the controller and closed-loop response are jointly synthesized and we cannot enforce controller-specific constraints without subjecting the closed-loop map to the same constraints.We demonstrate the importance of separating controller design from closed-loop design with an example in which communication delay and locality constraints cause standard SLS to be infeasible. Using our new two-step procedure, we are able to synthesize a controller that obeys the constraints while only incurring a 3% increase in LQR cost compared to the optimal LQR controller

Distributed Linear Quadratic Regulator Robust to Communication Dropouts

We present a solution to deal with information package dropouts in distributed controllers for large-scale networks. We do this by leveraging the System Level Synthesis approach, a control framework particularly suitable for large-scale networks that addresses information exchange in a very transparent manner. To this end, we propose two different schemes for controller synthesis and implementation. The first one synthesizes a controller inherently robust to dropouts, which is later implemented in an offline fashion. For the second approach, we synthesize a collection of controllers offline and then switch between different controllers online depending on the current dropouts detected in the system. The two approaches are illustrated and compared by means of a simulation example.Comment: Accepted contribution to the 21st World Congress of the International Federation of Automatic Control, 202

A System Level Approach to Discrete-Time Nonlinear Systems

In this paper, we will show that there is a universal connection between the closed-loop and the corresponding realizing controller in nonlinear discrete-time systems: Given an achievable stable closed-loop, we can follow a systematic procedure to construct an internally stable causal controller that realizes the desired closed-loop. In the linear system case, this relationship has been used as a key result in the recently developed System Level Synthesis (SLS), and this paper shows how this relationship finds its analogue in the general nonlinear discrete-time system case. Necessary and sufficient conditions are presented that characterize the entire space of closedloops that are achievable by some causal controller for a given system. Furthermore, we will show that constructing the same causal controller from maps that are not achievable closed-loops, still can stabilize the nonlinear system if they approximate the feasibility conditions well enough. Finally, we will discuss how this method opens up new ways towards robust nonlinear controller synthesis, by exploring two direct applications of this approach: design of trajectory tracking controllers for nonlinear systems using linear SLS controllers, and a method to stably "blend" multiple linear SLS controllers into one nonlinear controller that improves closed-loop performance. The companion paper [1] applies the latter approach to large-scale systems with actuator saturation and safety constraints

A System Level Approach to Discrete-Time Nonlinear Systems

In this paper, we will show that there is a universal connection between the closed-loop and the corresponding realizing controller in nonlinear discrete-time systems: Given an achievable stable closed-loop, we can follow a systematic procedure to construct an internally stable causal controller that realizes the desired closed-loop. In the linear system case, this relationship has been used as a key result in the recently developed System Level Synthesis (SLS), and this paper shows how this relationship finds its analogue in the general nonlinear discrete-time system case. Necessary and sufficient conditions are presented that characterize the entire space of closedloops that are achievable by some causal controller for a given system. Furthermore, we will show that constructing the same causal controller from maps that are not achievable closed-loops, still can stabilize the nonlinear system if they approximate the feasibility conditions well enough. Finally, we will discuss how this method opens up new ways towards robust nonlinear controller synthesis, by exploring two direct applications of this approach: design of trajectory tracking controllers for nonlinear systems using linear SLS controllers, and a method to stably "blend" multiple linear SLS controllers into one nonlinear controller that improves closed-loop performance. The companion paper [1] applies the latter approach to large-scale systems with actuator saturation and safety constraints