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Register a new userCombining Prior Knowledge and Data for Robust Controller Design
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We present a framework for systematically combining data of an unknown linear time-invariant system with prior knowledge on the system matrices or on the uncertainty for robust controller design. Our approach leads to linear matrix inequality (LMI) based feasibility criteria which guarantee stability and performance robustly for all closed-loop systems consistent with the prior knowledge and the available data. The design procedures rely on a combination of multipliers inferred via prior knowledge and learnt from measured data, where for the latter a novel and unifying disturbance description is employed. While large parts of the paper focus on linear systems and input-state measurements, we also provide extensions to robust output-feedback design based on noisy input-output data and against nonlinear uncertainties. We illustrate through numerical examples that our approach provides a flexible framework for simultaneously leveraging prior knowledge and data, thereby reducing conservatism and improving performance significantly if compared to black-box approaches to data-driven control.
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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.
Appropriate greenhouse temperature should be maintained to ensure crop production while minimizing energy consumption. Even though weather forecasts could provide a certain amount of information to improve control performance, it is not perfect and forecast error may cause the temperature to deviate from the acceptable range. To inherent uncertainty in weather that affects control accuracy, this paper develops a data-driven robust model predictive control (MPC) approach for greenhouse temperature control. The dynamic model is obtained from thermal resistance-capacitance modeling derived by the Building Resistance-Capacitance Modeling (BRCM) toolbox. Uncertainty sets of ambient temperature and solar radiation are captured by support vector clustering technique, and they are further tuned for better quality by training-calibration procedure. A case study that implements the carefully chosen uncertainty sets on robust model predictive control shows that the data-driven robust MPC has better control performance compared to rule-based control, certainty equivalent MPC, and robust MPC.
This paper presents an impedance control architecture for an electroacoustic absorber combining both a feedforward and feedback microphone-based system on a current driven loudspeaker. Feedforward systems enable good performance for direct impedance control. However, inaccuracies in the required actuator model can lead to a loss of passivity, which can cause unstable behaviors. The feedback contribution allows the absorber to better handle model errors and still achieve an accurate impedance. Numerical and experimental studies were conducted to compare this new architecture against a state-of-the-art feedforward control method.
Fast and accurate optimization and simulation is widely becoming a necessity for large scale transmission resiliency and planning studies such as N-1 SCOPF, batch contingency solvers, and stochastic power flow. Current commercial tools, however, prioritize speed of convergence over accuracy by relying on initial conditions that are taken from the steady state solution of similar network configurations that are not guaranteed to lie within a convex region of a valid solution. In this paper we introduce a globally convergent algorithm to facilitate fast and accurate AC steady state simulation and optimization based on prior knowledge from similar networks. The approach uses a homotopy method that gradually and efficiently translates a previously known network configuration to the current network configuration. The proposed formulation is highly scalable, and its efficacy is demonstrated for resiliency study and optimization of large networks up to 70k buses.
Systematic design and verification of advanced control strategies for complex systems under uncertainty largely remains an open problem. Despite the promise of blackbox optimization methods for automated controller tuning, they generally lack formal guarantees on the solution quality, which is especially important in the control of safety-critical systems. This paper focuses on obtaining closed-loop performance guarantees for automated controller tuning, which can be formulated as a black-box optimization problem under uncertainty. We use recent advances in non-convex scenario theory to provide a distribution-free bound on the probability of the closed-loop performance measures. To mitigate the computational complexity of the data-driven scenario optimization method, we restrict ourselves to a discrete set of candidate tuning parameters. We propose to generate these candidates using constrained Bayesian optimization run multiple times from different random seed points. We apply the proposed method for tuning an economic nonlinear model predictive controller for a semibatch reactor modeled by seven highly nonlinear differential equations.
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