arXiv subjects

Neelay Junnarkar

Publications and source records attributed to Neelay Junnarkar.

9 recordsLinked to original sources

arXiv2026

Learning Neural Network Controllers with Certified Robust Performance via Adversarial Training

Neural network (NN) controllers achieve strong empirical performance on nonlinear dynamical systems, yet deploying them in safety-critical settings requires robustness to disturbances and uncertainty. We present a method for jointly synthesizing NN controllers and dissipativity certificates that formally guarantee robust closed-loop performance using adversarial training, in which we use counterexamples to the robust dissipativity condition to guide training. Verification is done post-training using alpha,beta-CROWN, a branch-and-bound-based method that enables direct analysis of the nonlinear dynamical system. The proposed method uses quadratic constraints (QCs) only for characterization of non-parametric uncertainties. The method is tested in numerical experiments on maximizing the volume of the set on which a system is certified to be robustly dissipative. Our method certifies regions up to 78 times larger than the region certified by a linear matrix inequality-based approach that we derive for comparison.

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arXiv2026

Polynomial Constraints for Robustness Analysis of Nonlinear Systems

This paper presents a framework for abstracting uncertain or non-polynomial components of dynamical systems using polynomial constraints. This enables the application of polynomial-based analysis tools, such as sum-of-squares programming, to a broader class of non-polynomial systems. A numerical method for constructing these constraints is proposed. The relationship between polynomial constraints and existing integral quadratic constraints (IQCs) is investigated, providing transformations of IQCs into polynomial constraints. The effectiveness of polynomial constraints in characterizing nonlinearities is validated via numerical examples to compute inner estimates of the region of attraction for two systems.

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arXiv2024

Stability Margins of Neural Network Controllers

We present a method to train neural network controllers with guaranteed stability margins. The method is applicable to linear time-invariant plants interconnected with uncertainties and nonlinearities that are described by integral quadratic constraints. The type of stability margin we consider is the disk margin. Our training method alternates between a training step to maximize reward and a stability margin-enforcing step. In the stability margin enforcing-step, we solve a semidefinite program to project the controller into the set of controllers for which we can certify the desired disk margin.

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arXiv2024

Exploiting Symmetry in Dynamics for Model-Based Reinforcement Learning with Asymmetric Rewards

Recent work in reinforcement learning has leveraged symmetries in the model to improve sample efficiency in training a policy. A commonly used simplifying assumption is that the dynamics and reward both exhibit the same symmetry; however, in many real-world environments, the dynamical model exhibits symmetry independent of the reward model. In this paper, we assume only the dynamics exhibit symmetry, extending the scope of problems in reinforcement learning and learning in control theory to which symmetry techniques can be applied. We use Cartan's moving frame method to introduce a technique for learning dynamics that, by construction, exhibit specified symmetries. Numerical experiments demonstrate that the proposed method learns a more accurate dynamical model

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arXiv2024

Certifying Stability and Performance of Uncertain Differential-Algebraic Systems: A Dissipativity Framework

This paper presents a novel framework for characterizing dissipativity of uncertain systems whose dynamics evolve according to differential-algebraic equations. Sufficient conditions for dissipativity (specializing to, e.g., stability or $L_2$ gain bounds) are provided in the case that uncertainties are characterized by integral quadratic constraints. For polynomial or linear dynamics, these conditions can be efficiently verified through sum-of-squares or semidefinite programming. Performance analysis of the IEEE 39-bus power network with a set of potential line failures modeled as an uncertainty set provides an illustrative example that highlights the computational tractability of this approach; conservatism introduced in this example is shown to be quite minimal.

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arXiv2024

Grouping of $N-1$ Contingencies for Controller Synthesis: A Study for Power Line Failures

The problem of maintaining power system stability and performance after the failure of any single line in a power system (an "N-1 contingency") is investigated. Due to the large number of possible N-1 contingencies for a power network, it is impractical to optimize controller parameters for each possible contingency a priori. A method to partition a set of contingencies into groups of contingencies that are similar to each other from a control perspective is presented. Design of a single controller for each group, rather than for each contingency, provides a computationally tractable method for maintaining stability and performance after element failures. The choice of number of groups tunes a trade-off between computation time and controller performance for a given set of contingencies. Results are simulated on the IEEE 39-bus and 68-bus systems, illustrating that, with controllers designed for a relatively small number of groups, power system stability may be significantly improved after an N-1 contingency compared to continued use of the nominal controller. Furthermore, performance is comparable to that of controllers designed for each contingency individually.

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arXiv2024

Fast Assignment in Asset-Guarding Engagements using Function Approximation

This letter considers assignment problems consisting of n pursuers attempting to intercept n targets. We consider stationary targets as well as targets maneuvering toward an asset. The assignment algorithm relies on an n x n cost matrix where entry (i, j) is the minimum time for pursuer i to intercept target j. Each entry of this matrix requires the solution of a nonlinear optimal control problem. This subproblem is computationally intensive and hence the computational cost of the assignment is dominated by the construction of the cost matrix. We propose to use neural networks for function approximation of the minimum time until intercept. The neural networks are trained offline, thus allowing for real-time online construction of cost matrices. Moreover, the function approximators have sufficient accuracy to obtain reasonable solutions to the assignment problem. In most cases, the approximators achieve assignments with optimal worst case intercept time. The proposed approach is demonstrated on several examples with increasing numbers of pursuers and targets.

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arXiv2024

Synthesizing Neural Network Controllers with Closed-Loop Dissipativity Guarantees

This paper presents a method to synthesize neural network controllers to maximize reward subject to the hard constraint that the feedback system of plant and controller be dissipative, certifying requirements such as stability and $L_2$ gain bounds. It considers nonlinear and uncertain plants, modeled as the interconnection of a linear time-invariant (LTI) system and an uncertainty block, which incorporates nonlinearities. The uncertainty of the plant and the activation functions of the neural network are both described using integral quadratic constraints (IQCs). First, a dissipativity condition is derived for uncertain LTI systems. Second, this condition is used to construct a linear matrix inequality (LMI) which can be used to synthesize neural network controllers. Finally, this convex condition is used in a projection-based training method to synthesize neural network controllers with dissipativity guarantees. Numerical examples on an inverted pendulum and a flexible rod on a cart are provided to demonstrate the effectiveness of this approach.

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arXiv2022

Synthesis of Stabilizing Recurrent Equilibrium Network Controllers

We propose a parameterization of a nonlinear dynamic controller based on the recurrent equilibrium network, a generalization of the recurrent neural network. We derive constraints on the parameterization under which the controller guarantees exponential stability of a partially observed dynamical system with sector bounded nonlinearities. Finally, we present a method to synthesize this controller using projected policy gradient methods to maximize a reward function with arbitrary structure. The projection step involves the solution of convex optimization problems. We demonstrate the proposed method with simulated examples of controlling nonlinear plants, including plants modeled with neural networks.

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