arXiv subjects

Léa Ninite

Publications and source records attributed to Léa Ninite.

3 recordsLinked to original sources

arXiv2026

Iterative graph lifting for automatic design of path-complete stability certificates

Stability of switched linear systems under arbitrary switching is a fundamental problem in control theory, closely related to the joint spectral radius (JSR), which characterizes the worst-case growth rate of system trajectories. In this paper, we contribute to the path-complete approach for approximating the JSR. This framework constructs algebraic stability certificates using labeled directed graphs, known as path-complete graphs. These certificates can be computed via an associated optimization problem. We propose an iterative algorithm that refines path-complete graphs in an efficient and parsimonious manner. The algorithm relies on a graph-theoretic analysis of the optimality conditions of the underlying optimization problem. In particular, we derive a sufficient condition under which the exact JSR is attained by a given path-complete graph. When this condition is not satisfied, we identify bottleneck nodes by analyzing the graph induced by the active constraints. We then use this information to refine the path-complete graph via local graph lifting (node splitting), and repeat the procedure. Numerical experiments demonstrate the effectiveness and scalability of the proposed approach, outperforming state-of-the-art methods on all challenging instances tested.

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arXiv2026

Robust Optimal Control of Arbitrarily Switched Systems: A Path-Complete Framework

This paper addresses the robust control of switched systems under arbitrary switching with performance guarantees. We propose a framework that jointly synthesizes a feedback policy and a certified upper bound on its corresponding infinite-horizon closed-loop value function. The proposed upper bound not only certifies the performance of the synthesized policy, but can also be optimized during controller synthesis. More precisely, our approach associates functions with the nodes of a path-complete graph and enforces graph-based Bellman inequalities along its edges. Exploiting a newly introduced notion of reachability graph, these functions are combined into both a feedback policy and a certified upper bound on its corresponding closed-loop value function, expressed as a pointwise min-max combination of the graph-indexed functions. For linear switched systems with quadratic stage costs, the proposed framework admits tractable computational formulations based on semidefinite programming and alternating optimization. Numerical experiments, including a building temperature regulation benchmark, demonstrate the practical usefulness of the proposed approach both for direct feedback control using the synthesized policy and for model predictive control using the certified upper bound as a terminal cost.

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arXiv2026

A Path-Complete Approach for Optimal Control of Switched Systems

We study the problem of estimating the value function of discrete-time switched systems under arbitrary switching. Unlike the switched LQR problem, where both inputs and mode sequences are optimized, we consider the case where switching is exogenous. For such systems, the number of possible mode sequences grows exponentially with time, making the exact computation of the value function intractable. This motivates the development of tractable bounds that approximate it. We propose a novel framework, based on path-complete graphs, for constructing computable upper bounds on the value function. In this framework, multiple quadratic functions are combined through a directed graph that encodes dynamic programming inequalities, yielding convex and sound formulations. For example, for switched linear systems with quadratic cost, we derive tractable LMI-based formulations and provide computational complexity bounds. We further establish approximation guarantees for the upper bounds and show asymptotic non-conservativeness using concepts from graph theory. Finally, we extend the approach to controller synthesis for systems with affine control inputs and demonstrate its effectiveness on numerical examples.

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