arXiv subjects

Ram Padmanabhan

Publications and source records attributed to Ram Padmanabhan.

12 recordsLinked to original sources

arXiv2026

Finite-time Reachability for Constrained, Partially Uncontrolled Nonlinear Systems

This paper presents a technique to drive the state of a constrained nonlinear system to a specified target state in finite time, when the system suffers a partial loss in control authority. Our technique builds on a recent method to control constrained nonlinear systems by building a simple, linear driftless approximation at the initial state. We construct a partition of the finite time horizon into successively smaller intervals, and design controlled inputs based on the approximate dynamics in each partition. Under conditions that bound the length of the time horizon, we prove that these inputs result in bounded error from the target state in the original nonlinear system. As successive partitions of the time horizon become shorter, the error reduces to zero despite the effect of uncontrolled inputs. A simulation example on the model of a fighter jet demonstrates that the designed sequence of controlled inputs achieves the target state despite the system suffering a loss of control authority over one of its inputs.

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arXiv2026

Energetic Resilience under Temporal Logic Specifications

In environments with uncertainties or undesirable influences, control systems can require additional energy to achieve their task while remaining resilient to these influences. In this paper, we present an energetic resilience metric that quantifies the maximal additional energy used by a system under undesired effects, while satisfying complex specifications encoded through temporal logic. We prove that this metric satisfies properties that enable its computation even for compositions of these specifications, thus allowing considerations of sequential reachability and safety tasks. For specifications related to finite-horizon reachability and safety, we describe how synthesizing a control input and computing this metric reduces to solving efficient quadratic programs. Two case studies on a fighter-jet model and a planar mobile robot illustrate how the synthesized control inputs satisfy given specifications despite undesired and potentially adversarial effects. Further, we demonstrate how the energetic resilience metric varies with the initial state as well as the magnitude of undesired effects.

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arXiv2025

Online Learning of Deceptive Policies under Intermittent Observation

In supervisory control settings, autonomous systems are not monitored continuously. Instead, monitoring often occurs at sporadic intervals within known bounds. We study the problem of deception, where an agent pursues a private objective while remaining plausibly compliant with a supervisor's reference policy when observations occur. Motivated by the behavior of real, human supervisors, we situate the problem within Theory of Mind: the representation of what an observer believes and expects to see. We show that Theory of Mind can be repurposed to steer online reinforcement learning (RL) toward such deceptive behavior. We model the supervisor's expectations and distill from them a single, calibrated scalar -- the expected evidence of deviation if an observation were to happen now. This scalar combines how unlike the reference and current action distributions appear, with the agent's belief that an observation is imminent. Injected as a state-dependent weight into a KL-regularized policy improvement step within an online RL loop, this scalar informs a closed-form update that smoothly trades off self-interest and compliance, thus sidestepping hand-crafted or heuristic policies. In real-world, real-time hardware experiments on marine (ASV) and aerial (UAV) navigation, our ToM-guided RL runs online, achieves high return and success with observed-trace evidence calibrated to the supervisor's expectations.

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arXiv2025

Ignore Drift, Embrace Simplicity: Constrained Nonlinear Control through Driftless Approximation

We present a novel technique to drive a nonlinear system to reach a target state under input constraints. The proposed controller consists only of piecewise constant inputs, generated from a simple linear driftless approximation to the original nonlinear system. First, we construct this approximation using only the effect of the control input at the initial state. Next, we partition the time horizon into successively shorter intervals and show that optimal controllers for the linear driftless system result in a bounded error from a specified target state in the nonlinear system. We also derive conditions under which the input constraint is guaranteed to be satisfied. On applying the optimal control inputs, we show that the error monotonically converges to zero as the intervals become successively shorter, thus achieving arbitrary closeness to the target state with time. Using simulation examples on classical nonlinear systems, we illustrate how the presented technique is used to reach a target state while still satisfying input constraints. In particular, we show that our method completes the task even when assumptions of the underlying theory are violated.

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arXiv2025

Mode-Prefix-Based Control of Switched Linear Systems with Applications to Fault Tolerance

In this paper, we consider the problem of designing prefix-based optimal controllers for switched linear systems over finite horizons. This problem arises in fault-tolerant control, when system faults result in abrupt changes in dynamics. We consider a class of mode-prefix-based linear controllers that depend only on the history of the switching signal. The proposed optimal control problems seek to minimize both expected performance and worst-case performance over switching signals. We show that this problem can be reduced to a convex optimization problem. To this end, we synthesize one controller for each switching signal under a prefix constraint that ensures consistency between controllers. Then, system level synthesis is used to obtain a convex program in terms of the system-level parameters. In particular, it is shown that the prefix constraints are linear in terms of the system-level parameters. Finally, we apply this framework for optimal control of a fighter jet model suffering from system faults, illustrating how fault tolerance is ensured.

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arXiv2025

Analysis of the Unscented Transform Controller for Systems with Bounded Nonlinearities

In this paper, we present an analysis of the Unscented Transform Controller (UTC), a technique to control nonlinear systems motivated as a dual to the Unscented Kalman Filter (UKF). We consider linear, discrete-time systems augmented by a bounded nonlinear function of the state. For such systems, we review 1-step and N-step versions of the UTC. Using a Lyapunov-based analysis, we prove that the states and inputs converge to a bounded ball around the origin, whose radius depends on the bound on the nonlinearity. Using examples of a fighter jet model and a quadcopter, we demonstrate that the UTC achieves satisfactory regulation and tracking performance on these nonlinear models.

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arXiv2025

Approximate Energetic Resilience of Nonlinear Systems under Partial Loss of Control Authority

In this paper, we quantify the resilience of nonlinear dynamical systems by studying the increased energy used by all inputs of a system that suffers a partial loss of control authority, either through actuator malfunctions or through adversarial attacks. To quantify the maximal increase in energy, we introduce the notion of an energetic resilience metric. Prior work in this particular setting does not consider general nonlinear dynamical systems. In developing this framework, we first consider the special case of linear driftless systems and recall the energies in the control signal in the nominal and malfunctioning systems. Using these energies, we derive a bound on the energetic resilience metric. For general nonlinear systems, we first obtain a condition on the mean value of the control signal in both the nominal and malfunctioning systems, which allows us to approximate the energy in the control. We then obtain a worst-case approximation of this energy for the malfunctioning system, over all malfunctioning inputs. Assuming this approximation is exact, we derive bounds on the energetic resilience metric when control authority is lost over one actuator. A set of simulation examples demonstrate that the metric is useful in quantifying the resilience of the system without significant conservatism, despite the approximations used in obtaining control energies for nonlinear systems.

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arXiv2024

Energetic Resilience of Linear Driftless Systems

When a malfunction causes a control system to lose authority over a subset of its actuators, achieving a task may require spending additional energy in order to compensate for the effect of uncontrolled inputs. To understand this increase in energy, we introduce an energetic resilience metric that quantifies the maximal additional energy required to achieve finite-time regulation in linear driftless systems that suffer this malfunction. We first derive optimal control signals and minimum energies to achieve this task in both the nominal and malfunctioning systems. We then obtain a bound on the worst-case energy used by the malfunctioning system, and its exact expression in the special case of loss of authority over one actuator. Further considering this special case, we derive a bound on the metric for energetic resilience. A simulation example on a model of an underwater robot demonstrates that this bound is useful in quantifying the increased energy used by a system suffering such a malfunction.

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arXiv2024

How Much Reserve Fuel: Quantifying the Maximal Energy Cost of System Disturbances

Motivated by the design question of additional fuel needed to complete a task in an uncertain environment, this paper introduces metrics to quantify the maximal additional energy used by a control system in the presence of bounded disturbances when compared to a nominal, disturbance-free system. In particular, we consider the task of finite-time stabilization for a linear time-invariant system. We first derive the nominal energy required to achieve this task in a disturbance-free system, and then the worst-case energy over all feasible disturbances. The latter leads to an optimal control problem with a least-squares solution, and then an infinite-dimensional optimization problem where we derive an upper bound on the solution. The comparison of these energies is accomplished using additive and multiplicative metrics, and we derive analytical bounds on these metrics. Simulation examples on an ADMIRE fighter jet model demonstrate the practicability of these metrics, and their variation with the task hardness, a combination of the distance of the initial condition from the origin and the task completion time.

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arXiv2024

Multiple Estimation Models for Discrete-time Adaptive Iterative Learning Control

This article focuses on making discrete-time Adaptive Iterative Learning Control (ILC) more effective using multiple estimation models. Existing strategies use the tracking error to adjust the parametric estimates. Our strategy uses the last component of the identification error to tune these estimates of the model parameters. We prove that this strategy results in bounded estimates of the parameters, and bounded and convergent identification and tracking errors. We emphasize that the proof does not use the key technical lemma. Rather, it uses the properties of square-summable sequences. We extend this strategy to include multiple estimation models and show that all the signals are bounded, and the errors converge. It is also shown that this works whether we switch between the models at every instant and every iteration or at the end of every iteration. Simulation results demonstrate the efficacy of the proposed method with a faster convergence using multiple estimation models.

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arXiv2023

Discrete Robust Control of Robot Manipulators using an Uncertainty and Disturbance Estimator

This article presents the design of a robust observer based on the discrete-time formulation of Uncertainty and Disturbance Estimator (UDE), a well-known robust control technique, for the purpose of controlling robot manipulators. The design results in a complete closed-loop, robust, controller--observer structure. The observer incorporates the estimate of the overall uncertainty associated with the plant, in order to mimic its dynamics, and the control law is generated using an auxiliary error instead of state tracking error. A detailed qualitative and quantitative stability analysis is provided, and simulations are performed on the two-link robot manipulator system. Further, a comparative study with well-known control strategies for robot manipulators is presented. The results demonstrate the efficacy of the proposed technique, with better tracking performance and lower control energy compared to other strategies.

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arXiv2022

Analysis of Gradient Descent with Varying Step Sizes using Integral Quadratic Constraints

The framework of Integral Quadratic Constraints (IQCs) is used to perform an analysis of gradient descent with varying step sizes. Two performance metrics are considered: convergence rate and noise amplification. We assume that the step size is produced from a line search and varies in a known interval. Modeling the algorithm as a linear, parameter-varying (LPV) system, we construct a parameterized linear matrix inequality (LMI) condition that certifies algorithm performance, which is solved using a result for polytopic LPV systems. Our results provide convergence rate guarantees when the step size lies within a restricted interval. Moreover, we recover existing rate bounds when this interval reduces to a single point, i.e. a constant step size. Finally, we note that the convergence rate depends only on the condition number of the problem. In contrast, the noise amplification performance depends on the individual values of the strong convexity and smoothness parameters, and varies inversely with them for a fixed condition number.

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