arXiv subjects

Dimitar Ho

Publications and source records attributed to Dimitar Ho.

11 recordsLinked to original sources

arXiv2026

Consistent Model Chasing Is Minimax Optimal: The Exact Value of Scalar Adversarial Adaptive Control under Large Parametric Uncertainty

We solve exactly a fundamental problem of adaptive control against adversarial disturbances: regulate the scalar system $x_{t+1} = ax_t + u_t + w_t$, $x_0=0$, $\|w\|_\infty \le 1$, where the constant pole $a \in [-\Delta, \Delta]$ is unknown in sign and magnitude and $\Delta$ is arbitrarily large. Elementary as the system looks, the least worst-case peak $\|x\|_\infty$ that a causal controller can guarantee against an adversarial pair $(a, w)$ (the value of this game) has, to our knowledge, never been determined for any adaptive control problem with parametric uncertainty of arbitrary size under this criterion; existing theory supplies stability certificates, gain bounds, and regret rates, not the value. That value is $\gamma^\star(\Delta) = 1 + \Delta$ for every $\Delta>0$. The summand $1$ is the irreducible price of the disturbance, and $\Delta$ the exact price of a single, unavoidable identification spike. The optimal policy is certainty-equivalent deadbeat control at the midpoint of the set-membership consistent interval, an instance of the robust oracle $\times$ consistent model chasing architecture. The architecture is forced, not merely sufficient: writing $\theta_t := -u_t/x_t$ exhibits every causal controller as an oracle-selector composition, and optimality pins the selector to the midpoint at the critical histories. The standard tools, classical and modern, each fail quantifiably: probing is punished before it pays, commitment is fatal at sub-disturbance excitation once adaptation is necessary, optimism degenerates to tie-breaking or pays asymptotically at least twice the optimum, and regret certificates are blind to the worst-case peak in both directions. The optimal law contains no exploration mechanism, its learning purely passive. These results give the first exact optimality certificate for consistent model chasing as a design principle for adversarial adaptive control.

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arXiv2022

Online Adversarial Stabilization of Unknown Networked Systems

We investigate the problem of stabilizing an unknown networked linear system under communication constraints and adversarial disturbances. We propose the first provably stabilizing algorithm for the problem. The algorithm uses a distributed version of nested convex body chasing to maintain a consistent estimate of the network dynamics and applies system level synthesis to determine a distributed controller based on this estimated model. Our approach avoids the need for system identification and accommodates a broad class of communication delay while being fully distributed and scaling favorably with the number of subsystems.

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arXiv2021

Online Robust Control of Nonlinear Systems with Large Uncertainty

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.

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arXiv2021

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.

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arXiv2020

Robust Model-Free Learning and Control without Prior Knowledge

We present a simple model-free control algorithm that is able to robustly learn and stabilize an unknown discrete-time linear system with full control and state feedback subject to arbitrary bounded disturbance and noise sequences. The controller does not require any prior knowledge of the system dynamics, disturbances, or noise, yet it can guarantee robust stability and provides asymptotic and worst-case bounds on the state and input trajectories. To the best of our knowledge, this is the first model-free algorithm that comes with such robust stability guarantees without the need to make any prior assumptions about the system. We would like to highlight the new convex geometry-based approach taken towards robust stability analysis which served as a key enabler in our results. We will conclude with simulation results that show that despite the generality and simplicity, the controller demonstrates good closed-loop performance.

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arXiv2020

Achieving Performance and Safety in Large Scale Systems with Saturation using a Nonlinear System Level Synthesis Approach

We present a novel class of nonlinear controllers that interpolates among differently behaving linear controllers as a case study for recently proposed Linear and Nonlinear System Level Synthesis framework. The structure of the nonlinear controller allows for simultaneously satisfying performance and safety objectives defined for small- and large-disturbance regimes. The proposed controller is distributed, handles delays, sparse actuation, and localizes disturbances. We show our nonlinear controller always outperforms its linear counterpart for constrained LQR problems. We further demonstrate the anti-windup property of an augmented control strategy based on the proposed controller for saturated systems via simulation.

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arXiv2020

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.

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arXiv2020

A System Level Approach to Discrete-Time Nonlinear Systems

We will show that there is a universal connection between the achievable closed-loop dynamics and the corresponding feedback controller that produces it. This connection shows promise to lead to new methods for robust nonlinear control in discrete-time. We will show that, given a causal nonlinear discrete-time system and controller, the resulting closed-loop is a solution to a nonlinear operator equation. Conversely, any causal solution to the nonlinear operator equation is a closed-loop that can be achieved by some causal controller. Moreover, solutions can be substituted into a simple dynamic controller structure, which we will refer to as a system level controller, to obtain an implementation of the unique corresponding feedback controller. System level controllers could be an attractive approach for robust nonlinear control, as we will show that even when they are parametrized with approximate solutions to the operator equation, they can still produce robustly stable closed loops. We will provide theoretical results that state how grade of approximation and robust stability of the closed loop are related. Additionally, we will explore some first applications of our results. Using the cart-pole system as an illustrative example, we will derive how to design robust discrete-time trajectory tracking controllers for continuous-time nonlinear systems. Secondly, we will introduce a particular class of system level controller that shows to be particularly useful for linear systems with actuator saturation and state constraints. The special structure of the controller allows for simple stability and performance analysis of the closed-loop in presence of disturbances. A particular application to large-scale systems with actuator saturation and safety constraints is presented in our companion paper.

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arXiv2019

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. 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.

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arXiv2018

Passive-Aggressive Learning and Control

In this work, we investigate the problem of simultaneously learning and controlling a system subject to adversarial choices of disturbances and system parameters. We study the problem for a scalar system with $l_\infty$-norm bounded disturbances and system parameters constrained to lie in a known bounded convex polytope. We present a controller that is globally stabilizing and gives continuously improving bounds on the worst-case state deviation. The proposed controller simultaneously learns the system parameters and controls the system. The controller emerges naturally from an optimization problem and balances exploration and exploitation in such a way that it is able to efficiently stabilize unstable and adversarial system dynamics. Specifically, if the controller is faced with large uncertainty, the initial focus is on exploration, retrieving information about the system by applying state-feedback controllers with varying gains and signs. In a pre-specified bounded region around the origin, our control strategy can be seen as passive in the sense that it learns very little information. Only once the noise and/or system parameters act in an adversarial way, leading to the state exiting the aforementioned region for more than one time-step, our proposed controller behaves aggressively in that it is guaranteed to learn enough about the system to subsequently robustly stabilize it. We end by demonstrating the efficiency of our methods via numerical simulations.

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arXiv2018

Three Dimensional Aggregation of Magnetic Particles

Magnetic drug delivery is a promising therapeutic because of magnetic fields' ability to permeate unperturbed in human tissue. One of the long-standing challenges in magnetic drug delivery is the inability to generate 3D aggregation non-invasively within the interior of the body. Earnshaw's theorem, which proves the impossibility of creating an energetic minimum in a curl-free and divergence-free field such as a magnetic field. However, one of the assumptions of Earnshaw's theorem is a static field. Here we show that it is possible to utilize a dynamically changing field and a dissipative force such as the drag, which is generally present, to create a stable aggregation point for magnetic particles. We also introduce a theoretical framework for designing the suitable magnetic fields for controlling a given magnetic particle in a particular fluid. This framework enables accurate determination of the necessary parameters for aggregation across a wide variety of magnetic particles and across multiple biologically-relevant fluids. By coating magnetic particles with desired therapeutic agents or attaching them to cells, a new class of treatment methodologies can be created in therapies such as targeted drug delivery and cell-based therapies. By dynamically changing the aggregation point, agents can also be guided along a particular path in the body. This technique of using dissipative forces to create a stable 3D aggregation point for particles could possibly be extended to a broad range of applications such as microscopic and macroscopic manipulation, robotics, guided self-assembly, magnetic plasma confinement, tissue engineering, and ion traps for quantum computers.

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