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Register a new userUncertainty Inference with Applications to Control and Decision
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Added by
Xinjia Chen
Publication date
2020
fields
Informatics Engineering
and research's language is
English
Authors
Xinjia Chen
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In many areas of engineering and sciences, decision rules and control strategies are usually designed based on nominal values of relevant system parameters. To ensure that a control strategy or decision rule will work properly when the relevant parameters vary within certain range, it is crucial to investigate how the performance measure is affected by the variation of system parameters. In this paper, we demonstrate that such issue boils down to the study of the variation of functions of uncertainty. Motivated by this vision, we propose a general theory for inferring function of uncertainties. By virtue of such theory, we investigate concentration phenomenon of random vectors. We derive uniform exponential inequalities and multidimensional probabilistic inequalities for random vectors, which are substantially tighter as compared to existing ones. The probabilistic inequalities are applied to investigate the performance of control systems with real parametric uncertainty. It is demonstrated much more useful insights of control systems can be obtained. Moreover, the probabilistic inequalities offer performance analysis in a significantly less conservative way as compared to the classical deterministic worst-case method.
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This paper proposes a novel framework for resource-aware control design termed performance-barrier-based triggering. Given a feedback policy, along with a Lyapunov function certificate that guarantees its correctness, we examine the problem of designing its digital implementation through event-triggered control while ensuring a prescribed performance is met and triggers occur as sparingly as possible. Our methodology takes into account the performance residual, i.e., how well the system is doing in regards to the prescribed performance. Inspired by the notion of control barrier function, the trigger design allows the certificate to deviate from monotonically decreasing, with leeway specified as an increasing function of the performance residual, resulting in greater flexibility in prescribing update times. We study different types of performance specifications, with particular attention to quantifying the benefits of the proposed approach in the exponential case. We build on this to design intrinsically Zeno-free distributed triggers for network systems. A comparison of event-triggered approaches in a vehicle platooning problem shows how the proposed design meets the prescribed performance with a significantly lower number of controller updates.
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.
In this paper, we propose a chance constrained stochastic model predictive control scheme for reference tracking of distributed linear time-invariant systems with additive stochastic uncertainty. The chance constraints are reformulated analytically based on mean-variance information, where we design suitable Probabilistic Reachable Sets for constraint tightening. Furthermore, the chance constraints are proven to be satisfied in closed-loop operation. The design of an invariant set for tracking complements the controller and ensures convergence to arbitrary admissible reference points, while a conditional initialization scheme provides the fundamental property of recursive feasibility. The paper closes with a numerical example, highlighting the convergence to changing output references and empirical constraint satisfaction.
We study the problem of pathwise stochastic optimal control, where the optimization is performed for each fixed realisation of the driving noise, by phrasing the problem in terms of the optimal control of rough differential equations. We investigate the degeneracy phenomenon induced by directly controlling the coefficient of the noise term, and propose a simple procedure to resolve this degeneracy whilst retaining dynamic programming. As an application, we use pathwise stochastic control in the context of stochastic filtering to construct filters which are robust to parameter uncertainty, demonstrating an original application of rough path theory to statistics.
We apply the framework of optimal nonlinear control to steer the dynamics of a whole-brain network of FitzHugh-Nagumo oscillators. Its nodes correspond to the cortical areas of an atlas-based segmentation of the human cerebral cortex, and the inter-node coupling strengths are derived from Diffusion Tensor Imaging data of the connectome of the human brain. Nodes are coupled using an additive scheme without delays and are driven by background inputs with fixed mean and additive Gaussian noise. Optimal control inputs to nodes are determined by minimizing a cost functional that penalizes the deviations from a desired network dynamic, the control energy, and spatially non-sparse control inputs. Using the strength of the background input and the overall coupling strength as order parameters, the networks state-space decomposes into regions of low and high activity fixed points separated by a high amplitude limit cycle all of which qualitatively correspond to the states of an isolated network node. Along the borders, however, additional limit cycles, asynchronous states and multistability can be observed. Optimal control is applied to several state-switching and network synchronization tasks, and the results are compared to controllability measures from linear control theory for the same connectome. We find that intuitions from the latter about the roles of nodes in steering the network dynamics, which are solely based on connectome features, do not generally carry over to nonlinear systems, as had been previously implied. Instead, the role of nodes under optimal nonlinear control critically depends on the specified task and the systems location in state space. Our results shed new light on the controllability of brain network states and may serve as an inspiration for the design of new paradigms for non-invasive brain stimulation.
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