arXiv subjects

Romain Postoyan

Publications and source records attributed to Romain Postoyan.

At least 19 recordsLinked to original sources

arXiv2026

Robust stabilization with spiking neuronal communication

Neuromorphic engineering develops hardware and software systems inspired by biological neurons, with the goal of achieving energy-efficient, low-latency, robust, and adaptive computation, communication and control. Its potential impact on systems and control is significant, as it may enable novel approaches to control and estimation by leveraging brain-inspired computation and communication principles. In this context, we present a framework for the robust stabilization of a plant subject to disturbances when the communication between noisy sensors and the controller relies on spiking signals generated by neuron-inspired schemes. The communication scheme consists of a spike encoder on the sensors side, which is based on integrate-and-fire neurons that convert the analog plant output measurement into a spiking signal, and a spike decoder on the controller side inspired by synaptic processing to convert the received spiking signal into an analog signal. We provide design conditions on the spike decoder, the spike encoder as well as on the controller under which the closed-loop system exhibits a practical input-to-state stability property, where the adjustable parameters are the amplitudes of the spikes. The results are shown to be applicable to a class of nonlinear systems as well as to any stabilizable and detectable linear time-invariant system. Numerical simulations on a single-link manipulator illustrate the potential of the approach.

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arXiv2026

On robustness, input-to-state stability and backstepping for stochastic differential equations

We study conditions under which stability of the origin of stochastic differential equations is robust to small perturbations. We express robustness in two ways, firstly in the sense that stochastic stability is maintained under small parametric perturbations not exceeding a state-dependent bound vanishing at the origin but positive elsewhere, and secondly via stochastic input-to-state stability (ISS) which allows non-zero perturbations everywhere. We prove the former property assuming the existence of a Lyapunov function certifying stochastic stability of the nominal system. Under the same assumption, stochastic ISS holds under a suitable state-dependent perturbation scaling. Stochastic exponential stability is maintained under proportionally bounded perturbations and implies exponential ISS even without perturbation scaling. Finally, we propose a novel approach to stochastic integrator backstepping in pure-feedback form that uses the tools from our robustness analysis.

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arXiv2026

Value iteration with stopping criterion: finite iterations, stability, and near-optimality guarantees

Value iteration (VI) is a cornerstone of dynamic programming that allows computing near-optimal feedback laws for general plant dynamics and cost functions. In practice, however, it must be stopped after finitely many iterations. This raises the question of when to stop the algorithm so that the resulting policies and value functions achieve desirable properties, like given near-optimality bounds and stability. In this context, we study deterministic, discrete-time systems with infinite-horizon (possibly discounted) costs whose inputs are generated by VI. We equip VI with a generalized stopping criterion that encompasses existing choices while allowing new ones. Our aim is to analyze the properties of the policies and value functions at the final iteration. Under mild assumptions, we first show that VI indeed terminates in a finite number of iterations. We then establish that the final policies are stabilizing by properly designing the stopping criterion, and derive explicit near-optimality bounds characterized by this choice. These results offer a design framework for the stopping criteria that balances computational effort with stability and performance guarantees.

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arXiv2026

Discounted MPC and infinite-horizon optimal control under plant-model mismatch: Stability and suboptimality

We study closed-loop stability and suboptimality for MPC and infinite-horizon optimal control solved using a surrogate model that differs from the real plant. We employ a unified framework based on quadratic costs to analyze both finite- and infinite-horizon problems, encompassing discounted and undiscounted scenarios alike. Plant-model mismatch bounds proportional to states and controls are assumed, under which the origin remains an equilibrium. Under continuity of the model and cost-controllability, exponential stability of the closed loop can be guaranteed. Furthermore, we give a suboptimality bound for the closed-loop cost recovering the optimal cost of the surrogate. The results reveal a tradeoff between horizon length, discounting and plant-model mismatch. The robustness guarantees are uniform over the horizon length, meaning that larger horizons do not require successively smaller plant-model mismatch.

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arXiv2025

Observer Design for Networked Linear Systems with Fast and Slow Dynamics under Measurement Noise

This paper addresses the emulation-based observer design for networked control systems (NCS) with linear plants that operate at two time scales in the presence of measurement noise. The system is formulated as a hybrid singularly perturbed dynamical system, enabling the systematic use of singular perturbation techniques to derive explicit bounds on the maximum allowable transmission intervals (MATI) for both fast and slow communication channels. Under the resulting conditions, the proposed observer guarantees that the estimation error satisfies a global exponential derivative-input-to-state stability (DISS)-like property, where the ultimate bound scales proportionally with the magnitudes of the measurement noise and the time derivative of the control input. The effectiveness of the approach is illustrated through a numerical example.

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arXiv2025

Discounted LQR: stabilizing (near-)optimal state-feedback laws

We study deterministic, discrete linear time-invariant systems with infinite-horizon discounted quadratic cost. It is well-known that standard stabilizability and detectability properties are not enough in general to conclude stability properties for the system in closed-loop with the optimal controller when the discount factor is small. In this context, we first review some of the stability conditions based on the optimal value function found in the learning and control literature and highlight their conservatism. We then propose novel (necessary and) sufficient conditions, still based on the optimal value function, under which stability of the origin for the optimal closed-loop system is guaranteed. Afterwards, we focus on the scenario where the optimal feedback law is not stabilizing because of the discount factor and the goal is to design an alternative stabilizing near-optimal static state-feedback law. We present both linear matrix inequality-based conditions and a variant of policy iteration to construct such stabilizing near-optimal controllers. The methods are illustrated via numerical examples.

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arXiv2025

An optimistic planning algorithm for switched discrete-time LQR

We introduce TROOP, a tree-based Riccati optimistic online planner, that is designed to generate near-optimal control laws for discrete-time switched linear systems with switched quadratic costs. The key challenge that we address is balancing computational resources against control performance, which is important as constructing near-optimal inputs often requires substantial amount of computations. TROOP addresses this trade-off by adopting an online best-first search strategy inspired by A*, allowing for efficient estimates of the optimal value function. The control laws obtained guarantee both near-optimality and stability properties for the closed-loop system. These properties depend on the planning depth, which determines how far into the future the algorithm explores and is closely related to the amount of computations. TROOP thus strikes a balance between computational efficiency and control performance, which is illustrated by numerical simulations on an example.

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arXiv2025

Robust Recurrence of Discrete-Time Infinite-Horizon Stochastic Optimal Control with Discounted Cost

We analyze the stability of general nonlinear discrete-time stochastic systems controlled by optimal inputs that minimize an infinite-horizon discounted cost. Under a novel stochastic formulation of cost-controllability and detectability assumptions inspired by the related literature on deterministic systems, we prove that uniform semi-global practical recurrence holds for the closed-loop system, where the adjustable parameter is the discount factor. Under additional continuity assumptions, we further prove that this property is robust.

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arXiv2025

Stabilization of singularly perturbed networked control systems over a single channel

This paper studies the emulation-based stabilization of nonlinear networked control systems with two time scales. We address the challenge of using a single communication channel for transmitting both fast and slow variables between the plant and the controller. A novel dual clock mechanism is proposed to schedule transmissions for this purpose. The system is modeled as a hybrid singularly perturbed dynamical system, and singular perturbation analysis is employed to determine individual maximum allowable transmission intervals for both fast and slow variables, ensuring semi-global practical asymptotic stability. Enhanced stability guarantees are also provided under stronger assumptions. The efficacy of the proposed method is illustrated through a numerical example.

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arXiv2024

Mixed Regular and Impulsive Sampled-data LQR

We investigate the benefits of combining regular and impulsive inputs for the control of sampled-data linear time-invariant systems. We first observe that adding an impulsive term to a regular, zero-order-hold controller may help enlarging the set of sampling periods under which controllability is preserved by sampling. In this context, we provide a tailored Hautus-like necessary and sufficient condition under which controllability of the mixed regular, impulsive (MRI) sampled-data model is preserved. We then focus on LQR optimal control. After having presented the optimal controllers for the sampled-data LQR control in the MRI setting, we consider the scenario where an impulsive disturbance affects the dynamics and is known ahead of time. The solution to the so-called preview LQR is presented exploiting both regular and impulsive input components. Numerical examples, that include an insulin infusion benchmark, illustrate that leveraging both future disturbance information and MRI controls may lead to significant performance improvements.

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arXiv2024

Discrete-Time Conewise Linear Systems with Finitely Many Switches

We investigate discrete-time conewise linear systems (CLS) for which all the solutions exhibit a finite number of switches. By switches, we mean transitions of a solution from one cone to another. Our interest in this class of CLS comes from the optimization-based control of an insulin infusion model for which the fact that solutions switch finitely many times appears to be key to establish the global exponential stability of the origin. The stability analysis of this class of CLS greatly simplifies compared to general CLS as all solutions eventually exhibit linear dynamics. The main challenge is to characterize CLS satisfying this finite number of switches property. We first present general conditions in terms of set intersections for this purpose. To ease the testing of these conditions, we translate them as a non-negativity test of linear forms using Farkas lemma. As a result, the problem reduces to verify the non-negativity of a single solution to an auxiliary linear discrete-time system. Interestingly, this property differs from the classical non-negativity problem, where any solution to a system must remain non-negative (component-wise) for any non-negative initial condition, and thus requires novel tools to test it. We finally illustrate the relevance of the presented results on the optimal insulin infusion problem.

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arXiv2024

A hybrid systems framework for data-based adaptive control of linear time-varying systems

We consider the data-driven stabilization of discrete-time linear time-varying systems. The controller is defined as a linear state-feedback law whose gain is adapted to the plant changes through a data-based event-triggering rule. To do so, we monitor the evolution of a data-based Lyapunov function along the solution. When this Lyapunov function does not satisfy a designed desirable condition, an episode is triggered to update the controller gain and the corresponding Lyapunov function using the last collected data. The resulting closed-loop dynamics hence exhibits both physical jumps, due to the system dynamics, and episodic jumps, which naturally leads to a hybrid discrete-time system. We leverage the inherent robustness of the controller and provide general conditions under which various stability notions can be established for the system. Two notable cases where these conditions are satisfied are treated, and numerical results illustrating the relevance of the approach are discussed.

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arXiv2024

Policy iteration for discrete-time systems with discounted costs: stability and near-optimality guarantees

Given a discounted cost, we study deterministic discrete-time systems whose inputs are generated by policy iteration (PI). We provide novel near-optimality and stability properties, while allowing for non stabilizing initial policies. That is, we first give novel bounds on the mismatch between the value function generated by PI and the optimal value function, which are less conservative in general than those encountered in the dynamic programming literature for the considered class of systems. Then, we show that the system in closed-loop with policies generated by PI are stabilizing under mild conditions, after a finite (and known) number of iterations.

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arXiv2024

Hybrid low-dimensional limiting state of charge estimator for multi-cell lithium-ion batteries

The state of charge (SOC) of lithium-ion batteries needs to be accurately estimated for safety and reliability purposes. For battery packs made of a large number of cells, it is not always feasible to design one SOC estimator per cell due to limited computational resources. Instead, only the minimum and the maximum SOC need to be estimated. The challenge is that the cells having minimum and maximum SOC typically change over time. In this context, we present a low-dimensional hybrid estimator of the minimum (maximum) SOC, whose convergence is analytically guaranteed. We consider for this purpose a battery consisting of cells interconnected in series, which we model by electric equivalent circuit models. We then present the hybrid estimator, which runs an observer designed for a single cell at any time instant, selected by a switching-like logic mechanism. We establish a practical exponential stability property for the estimation error on the minimum (maximum) SOC thereby guaranteeing the ability of the hybrid scheme to generate accurate estimates of the minimum (maximum) SOC. The analysis relies on non-smooth hybrid Lyapunov techniques. A numerical illustration is provided to showcase the relevance of the proposed approach.

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arXiv2023

Hybrid coupling rules for leaderless heterogeneous oscillators: uniform global asymptotic and finite-time synchronization

We investigate the engineering scenario where the objective is to synchronize heterogeneous oscillators in a distributed fashion. The internal dynamics of each oscillator are general enough to capture their time-varying natural frequency as well as physical couplings and unknown bounded terms. A communication layer is set in place to allow the oscillators to exchange synchronizing coupling actions through a tree-like leaderless network. In particular, we present a class of hybrid coupling rules depending only on local information to ensure uniform global practical or asymptotic synchronization, which is impossible to obtain by using the Kuramoto model customarily used in the literature. We further show that the synchronization set can be made uniformly globally prescribed finite-time stable by selecting the coupling function to be discontinuous at the origin. Novel mathematical tools on non-pathological functions and set-valued Lie derivatives are developed to carry out the stability analysis. The effectiveness of the approach is illustrated in simulations where we apply our synchronizing hybrid coupling rules to models of power grids previously used in the literature.

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arXiv2023

Enhancing accuracy of finite-dimensional models for lithium-ion batteries, observer design and experimental validation

Accurate estimation of the internal states of lithium-ion batteries is key towards improving their management for safety, efficiency and longevity purposes. Various approaches exist in the literature in this context, among which designing an observer based on an electrochemical model of the battery dynamics. With this approach, the performance of the observer depends on the accuracy of the considered model. It appears that electrochemical models, and thus their associated observer, typically require to be of high dimension to generate accurate internal variables. In this work, we present a method to mitigate this limitation by correcting the lithium concentrations generated by a general class of finite-dimensional electrochemical models such that they asymptotically match those generated by the original partial differential equations (PDE) they are based on, for constant input currents. These corrections apply irrespectively of the order of the considered finite-dimensional model. The proposed correction leads to a new state space model for which we design observers, whose global, robust convergences are supported by a Lyapunov analysis. Both numerical and experimental validations are presented, which show the improvement of the accuracy of the state estimates as a result of the proposed corrections.

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arXiv2023

Finite-time stability properties of Lur'e systems with piecewise continuous nonlinearities

We analyze the stability properties of Lur'e systems with piecewise continuous nonlinearities by exploiting the notion of set-valued Lie derivative for Lur'e-Postnikov Lyapunov functions. We first extend an existing result of the literature to establish the global asymptotic stability of the origin under a more general sector condition. We then present the main results of this work, namely additional conditions under which output and state finite-time stability properties also hold for the considered class of systems. We highlight the relevance of these results by certifying the stability properties of two engineering systems of known interest: mechanical systems affected by friction and cellular neural networks.

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arXiv2022

Transmit power policies for stochastic stabilisation of multi-link wireless networked control systems

Transmit power control is one of the most important issues in wireless networks, where nodes typically operate on limited battery power. Reducing communicating power consumption is essential for both economic and ecologic reasons. In fact, transmitting at unnecessarily high power not only reduces node lifetime, but also introduces excessive interference and electromagnetic pollution. Existing work in the wireless community mostly focus on designing transmit power policies by taking into account communication aspects like quality of service or network capacity. Wireless networked control systems (WNCSs), on the other hand, have different and specific needs such as stability, which require transmit power policies adapted to the control context. Transmit power design in the control community has recently attracted much attention, and available works mostly consider linear systems or specific classes of non-linear systems with a single-link view of the system. In this paper, we propose a framework for the design of stabilising transmit power levels that applies to much larger classes of non-linear plants, controllers, and multi-link setting. By exploiting the fact that channel success probabilities are related to transmit power in a non-linear fashion, we first derive closed-loop stability conditions that relate channel probabilities with transmission rate. Next, we combine these results together with well-known and realistic interference models to provide a design methodology for stabilising transmit power in non-linear and multi-link WNCSs.

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