arXiv subjects

Leila Bridgeman

Publications and source records attributed to Leila Bridgeman.

14 recordsLinked to original sources

arXiv2026

Data driven synthesis of provable invariant sets via stochastically sampled data

Positive invariant (PI) sets are essential for ensuring safety, i.e. constraint adherence, of dynamical systems. With the increasing availability of sampled data from complex (and often unmodeled) systems, it is advantageous to leverage these data sets for PI set synthesis. This paper uses data driven geometric conditions of invariance to synthesize PI sets from data. Where previous data driven, set-based approaches to PI set synthesis used deterministic sampling schemes, this work instead synthesizes PI sets from any pre-collected data sets. Beyond a data set and Lipschitz continuity, no additional information about the system is needed. A tree data structure is used to partition the space and select samples used to construct the PI set, while Lipschitz continuity is used to provide deterministic guarantees of invariance. Finally, probabilistic bounds are given on the number of samples needed for the algorithm to determine of a certain volume.

eess.SY↗

arXiv2026

Adaptive Meshing for CPA Lyapunov Function Synthesis

Continuous Piecewise Affine (CPA) Lyapunov function synthesis is one method to perform Lyapunov stability analysis for nonlinear systems. This method first generates a mesh over the region of interest in the system's state space and then solves a linear program (LP), which enforces constraints on each vertex of the mesh, to synthesize a Lyapunov function. Finer meshes broaden the class of Lyapunov function candidates, but CPA function synthesis is more computationally expensive for finer meshes -- particularly so in higher dimensional systems. This paper explores methods to mesh the region of interest more efficiently so that a Lyapunov function can be synthesized using less computational effort. Three methods are explored -- adaptive meshing, meshing using knowledge of the system model, and a combination of the two. Numerical examples for two and three dimensional nonlinear dynamical systems are used to compare the efficacy of the three methods.

eess.SY↗

arXiv2025

Local Dissipativity Analysis of Nonlinear Systems

Dissipativity is an input-output (IO) characterization of nonlinear systems that enables compositional robust control through Vidyasagar's Network Dissipativity Theorem (VDNT). However, determining the dissipativity of a system is an involved and, often, model-specific process. We present a general method to determine the local dissipativity properties of smooth, nonlinear, control affine systems. We simultaneously search for the optimal IO characterization of a system and synthesize a continuous piecewise affine (CPA) storage function via a convex optimization problem. To do so, we reformulate the dissipation inequality as a matrix inequality (MI) and develop novel linear matrix inequality (LMI) bounds for a triangulation to impose the dissipativity conditions on the CPA storage function Further, we develop a method to synthesize a combined quadratic and CPA storage function to expand the systems the optimization problem is applicable to. Finally, we establish that our method will always find a feasible IO characterization and storage function given that the system is sufficiently strictly locally dissipative and demonstrate the efficacy of our method in determining the conic bounds and gain of various nonlinear systems.

eess.SY↗

arXiv2025

Learning Control Barrier Functions with Deterministic Safety Guarantees

Barrier functions (BFs) characterize safe sets of dynamical systems, where hard constraints are never violated as the system evolves over time. Computing a valid safe set and BF for a nonlinear (and potentially unmodeled), non-autonomous dynamical system is a difficult task. This work explores the design of BFs using data to obtain safe sets with deterministic assurances of control invariance. We leverage ReLU neural networks (NNs) to create continuous piecewise affine (CPA) BFs with deterministic safety guarantees for Lipschitz continuous, discrete-time dynamical system using sampled one-step trajectories. The CPA structure admits a novel classifier term to create a relaxed \ac{bf} condition and construction via a data driven constrained optimization. We use iterative convex overbounding (ICO) to solve this nonconvex optimization problem through a series of convex optimization steps. We then demonstrate our method's efficacy on two-dimensional autonomous and non-autonomous dynamical systems.

eess.SY↗

arXiv2025

Dissipativity-Based Distributed Stability Analysis for Networks with Heterogeneous Nonlinear Agents

Stabilizing large networks of nonlinear agents is challenging; decomposition and distributed analysis of these networks are crucial for computational tractability and information security. Vidyasagar's Network Dissipativity Theorem enables both properties concurrently in distributed network analysis. This paper explored combining it with the alternating direction methods of multipliers to develop distributed stability analysis for networks of inhomogeneous, nonlinear agents. One algorithm enhances information security by requiring agents to share only a dissipativity characterization, not a dynamical model, for stability analysis. A second algorithm further restricts this information sharing to their clique, thereby enhancing security, and can also reduce the computational burden of stability analysis if the network allows chordal decomposition. The convergence of the proposed algorithms is demonstrated, and criteria are identified for decomposable networks facilitating chordal decomposition. The effectiveness of the proposed methods is demonstrated through numerical examples involving a swarm of linearized unmanned aerial vehicles and networks beyond linear time-invariant agents.

eess.SY↗

arXiv2025

Consensus-Based Stability Analysis of Multi-Agent Networks

The emergence of large-scale multi-agent systems has led to controller synthesis methods for sparse communication between agents. However, most sparse controller synthesis algorithms remain centralized, requiring information exchange and high computational costs. This underscores the need for distributed algorithms that design controllers using only local dynamics information from each agent. This paper presents a consensus-based distributed stability analysis. The proposed stability analysis algorithms leverage Vidyasagar's Network Dissipativity Theorem and the alternating direction methods of multipliers to perform general stability analysis. Numerical examples involving a 2D swarm of unmanned aerial vehicles demonstrate the convergence of the proposed algorithms.

eess.SY↗

arXiv2025

TumorMap: A Laser-based Surgical Platform for 3D Tumor Mapping and Fully-Automated Tumor Resection

Surgical resection of malignant solid tumors is critically dependent on the surgeon's ability to accurately identify pathological tissue and remove the tumor while preserving surrounding healthy structures. However, building an intraoperative 3D tumor model for subsequent removal faces major challenges due to the lack of high-fidelity tumor reconstruction, difficulties in developing generalized tissue models to handle the inherent complexities of tumor diagnosis, and the natural physical limitations of bimanual operation, physiologic tremor, and fatigue creep during surgery. To overcome these challenges, we introduce "TumorMap", a surgical robotic platform to formulate intraoperative 3D tumor boundaries and achieve autonomous tissue resection using a set of multifunctional lasers. TumorMap integrates a three-laser mechanism (optical coherence tomography, laser-induced endogenous fluorescence, and cutting laser scalpel) combined with deep learning models to achieve fully-automated and noncontact tumor resection. We validated TumorMap in murine osteoscarcoma and soft-tissue sarcoma tumor models, and established a novel histopathological workflow to estimate sensor performance. With submillimeter laser resection accuracy, we demonstrated multimodal sensor-guided autonomous tumor surgery without any human intervention.

cs.RO↗

arXiv2024

Issues with Input-Space Representation in Nonlinear Data-Based Dissipativity Estimation

In data-based control, dissipativity can be a powerful tool for attaining stability guarantees for nonlinear systems if that dissipativity can be inferred from data. This work provides a tutorial on several existing methods for data-based dissipativity estimation of nonlinear systems. The interplay between the underlying assumptions of these methods and their sample complexity is investigated. It is shown that methods based on delta-covering result in an intractable trade-off between sample complexity and robustness. A new method is proposed to quantify the robustness of machine learning-based dissipativity estimation. It is shown that this method achieves a more tractable trade-off between robustness and sample complexity. Several numerical case studies demonstrate the results.

eess.SY↗

arXiv2024

Stochastic Dissipativity for Systems with Probabilistic Input Delays

This work considers stochastic operators in general inner-product spaces, and in particular, systems with stochastically time-varying input delays of a known probability distribution. Stochastic dissipativity and stability are defined from an operator-theoretic perspective, and the well-known open-loop dissipativity conditions for closed-loop/network stability are extended to the stochastic case. Criteria are derived to identify dissipative nonlinear systems with stochastic input delays, and this result is used to find delay-distribution-dependent linear matrix inequality conditions for stochastic dissipativity of a linear system with input delays of a known probability distribution. A numerical experiment demonstrates the utility of the resulting criteria for robust plant analysis and controller design, highlighting significantly reduced conservatism compared to deterministic methods.

math.OC↗

arXiv2022

Dissipative Imitation Learning for Robust Dynamic Output Feedback

Robust imitation learning seeks to mimic expert controller behavior while ensuring stability, but current methods require accurate plant models. Here, robust imitation learning is addressed for stabilizing poorly modeled plants with linear dynamic output feedback. Open-loop input-output properties are used to characterize an uncertain plant, and the feedback matrix of the dynamic controller is learned while enforcing stability through the controller's open-loop QSR-dissipativity properties. The imitation learning method is applied to two systems with parametric uncertainty.

eess.SY↗

arXiv2022

Systematic, Lyapunov-Based, Safe and Stabilizing Controller Synthesis for Constrained Nonlinear Systems

A controller synthesis method for state- and input-constrained nonlinear systems is presented that seeks continuous piecewise affine (CPA) Lyapunov-like functions and controllers simultaneously. Non-convex optimization problems are formulated on triangulated subsets of the admissible states that can be refined to meet primary control objectives, such as stability and safety, alongside secondary performance objectives. A multi-stage design is also given that enlarges the region of attraction (ROA) sequentially while allowing exclusive performance for each stage. A clear boundary for an invariant subset of closed-loop system's ROA is obtained from the resulting Lipschitz Lyapunov function. For control-affine nonlinear systems, the non-convex problem is formulated as a series of conservative, but well-posed, semi-definite programs. These decrease the cost function iteratively until the design objectives are met. Since the resulting CPA Lyapunov-like functions are also Lipschitz control (or barrier) Lyapunov functions, they can be used in online quadratic programming to find minimum-norm control inputs. Numerical examples are provided to demonstrate the effectiveness of the method.

eess.SY↗

arXiv2022

Systematic Stabilization of Constrained Piecewise Affine Systems

This paper presents an efficient, offline method to simultaneously synthesize controllers and seek closed-loop Lyapunov functions for constrained piecewise affine systems on triangulated subsets of the admissible states. Triangulation refinements explore a rich class of controllers and Lyapunov functions. Since an explicit Lipschitz Lyapunov function is found, an invariant subset of the closed-loop region of attraction is obtained. Moreover, it is a control Lyapunov function, so minimum-norm controllers can be realized through online quadratic programming. It is formulated as a sequence of semi-definite programs. The method avoids computationally burdensome non-convex optimizations and a-priori design choices that are typical of similar existing methods.

eess.SY↗

arXiv2021

Simultaneous Controller and Lyapunov Function Design for Constrained Nonlinear Systems

This paper presents a method to stabilize state and input constrained nonlinear systems using an offline optimization on variable triangulations of the set of admissible states. For control-affine systems, by choosing a continuous piecewise affine (CPA) controller structure, the non-convex optimization is formulated as iterative semi-definite programming (SDP), which can be solved efficiently using available software. The method has very general assumptions on the system's dynamics and constraints. Unlike similar existing methods, it avoids finding terminal invariant sets, solving non-convex optimizations, and does not rely on knowing a control Lyapunov function (CLF), as it finds a CPA Lyapunov function explicitly. The method enforces a desired upper-bound on the decay rate of the state norm and finds the exact region of attraction. Thus, it can be also viewed as a systematic approach for finding Lipschitz CLFs in state and input constrained control-affine systems. Using the CLF, a minimum norm controller is also formulated by quadratic programming for online application.

eess.SY↗

arXiv2021

Fixed-Order H2-Conic Control

H2-conic controller design seeks to minimize the closed-loop H2-norm for a nominal linear system while satisfying the Conic Sector Theorem for nonlinear stability. This problem has only been posed with limited design freedom, as opposed to fixed-order design where all controller parameters except the number of state estimates are free variables. Here, the fixed-order H2-conic design problem is reformulated as a convergent series of convex approximations using iterative convex overbounding. A synthesis algorithm and various initializations are proposed. The synthesis is applied to a passivity-violated system with uncertain parameters and compared to benchmark controller designs.

math.OC↗