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Register a new userCompetitive Control with Delayed Imperfect Information
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Added by
Chenkai Yu
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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This paper studies the impact of imperfect information in online control with adversarial disturbances. In particular, we consider both delayed state feedback and inexact predictions of future disturbances. We introduce a greedy, myopic policy that yields a constant competitive ratio against the offline optimal policy with delayed feedback and inexact predictions. A special case of our result is a constant competitive policy for the case of exact predictions and no delay, a previously open problem. We also analyze the fundamental limits of online control with limited information by showing that our competitive ratio bounds for the greedy, myopic policy in the adversarial setting match (up to lower-order terms) lower bounds in the stochastic setting.
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This paper presents competitive algorithms for a novel class of online optimization problems with memory. We consider a setting where the learner seeks to minimize the sum of a hitting cost and a switching cost that depends on the previous $p$ decisions. This setting generalizes Smoothed Online Convex Optimization. The proposed approach, Optimistic Regularized Online Balanced Descent, achieves a constant, dimension-free competitive ratio. Further, we show a connection between online optimization with memory and online control with adversarial disturbances. This connection, in turn, leads to a new constant-competitive policy for a rich class of online control problems.
This paper studies an optimal consensus problem for a group of heterogeneous high-order agents with unknown control directions. Compared with existing consensus results, the consensus point is further required to an optimal solution to some distributed optimization problem. To solve this problem, we first augment each agent with an optimal signal generator to reproduce the global optimal point of the given distributed optimization problem, and then complete the global optimal consensus design by developing some adaptive tracking controllers for these augmented agents. Moreover, we present an extension when only real-time gradients are available. The trajectories of all agents in both cases are shown to be well-defined and achieve the expected consensus on the optimal point. Two numerical examples are given to verify the efficacy of our algorithms.
The wake effect is one of the leading causes of energy losses in offshore wind farms (WFs). Both turbine placement and cooperative control can influence the wake interactions inside the WF and thus the overall WF power production. Traditionally, greedy control strategy is assumed in the layout design phase. To exploit the potential synergy between the WF layout and control so that a system-level optimal layout can be obtained with the greatest energy yields, the layout optimization should be performed with cooperative control considerations. For this purpose, a novel two-stage WF layout optimization model is developed in this paper. Cooperative WF control of both turbine yaw and axis-induction are considered. However, the integration of WF control makes the layout optimization much more complicated and results in a large-scale nonconvex problem, hindering the application of current layout optimization methods. To increase the computational efficiency, we leverage the hierarchy and decomposability of the joint optimization problem and design a decomposition-based hybrid method (DBHM). Case studies are carried out on different WFs. It is shown that WF layouts with higher energy yields can be obtained by the proposed joint optimization compared to traditional separate layout optimization. Moreover, the computational advantages of the proposed DBHM on the considered joint layout optimization problem are also demonstrated.
Robust control is a core approach for controlling systems with performance guarantees that are robust to modeling error, and is widely used in real-world systems. However, current robust control approaches can only handle small system uncertainty, and thus require significant effort in system identification prior to controller design. We present an online approach that robustly controls a nonlinear system under large model uncertainty. Our approach is based on decomposing the problem into two sub-problems, robust control design (which assumes small model uncertainty) and chasing consistent models, which can be solved using existing tools from control theory and online learning, respectively. We provide a learning convergence analysis that yields a finite mistake bound on the number of times performance requirements are not met and can provide strong safety guarantees, by bounding the worst-case state deviation. To the best of our knowledge, this is the first approach for online robust control of nonlinear systems with such learning theoretic and safety guarantees. We also show how to instantiate this framework for general robotic systems, demonstrating the practicality of our approach.
We study a class of deterministic finite-horizon two-player nonzero-sum differential games where players are endowed with different kinds of controls. We assume that Player 1 uses piecewise-continuous controls, while Player 2 uses impulse controls. For this class of games, we seek to derive conditions for the existence of feedback Nash equilibrium strategies for the players. More specifically, we provide a verification theorem for identifying such equilibrium strategies, using the Hamilton-Jacobi-Bellman (HJB) equations for Player 1 and the quasi-variational inequalities (QVIs) for Player 2. Further, we show that the equilibrium number of interventions by Player 2 is upper bounded. Furthermore, we specialize the obtained results to a scalar two-player linear-quadratic differential game. In this game, Player 1s objective is to drive the state variable towards a specific target value, and Player 2 has a similar objective with a different target value. We provide, for the first time, an analytical characterization of the feedback Nash equilibrium in a linear-quadratic differential game with impulse control. We illustrate our results using numerical experiments.
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