Hybrid Dynamical System Theory Research Articles

On Hybrid Prescribed-Time Concurrent Learning with Switching Datasets

We introduce a novel concurrent learning (CL) algorithm designed to solve parameter estimation problems within a user-prescribed time frame and by utilizing alternating datasets during the learning process. The algorithm can tackle applications involving switching data sets (including data sets that are completely uninformative) that are updated in real-time as the algorithm operates. To achieve parameter estimation within a specified time independent of the dataset’s richness, the switching algorithm employs dynamic gains. The main result establishes uniform global exponential ultimate boundedness, with an ultimate bound that shrinks to zero as the magnitude of the measurement disturbances decreases. The stability analysis leverages tools from hybrid dynamical systems theory, along with a recently introduced dilation/contraction argument on the hybrid time domains of the solutions. The algorithm and main results are illustrated via a numerical example.

Three Time-Scale Singular Perturbation Hybrid Control and Large-Signal Analysis Stability in AC-Microgrids

This work is devoted to propose a distributed control hybrid algorithm for the primary and secondary control loops of AC-bus microgrids in islanded mode and to provide a large-signal stability. A primary control loop based on Hybrid Dynamical System (HDS) theory manages the DC/AC inverters considering structural non-linearities in the model (affine terms and hybrid dynamics of their signals) and implementation constraints (dwell-time) and ensures the robustness of the output voltage with respect to any model variation. Moreover, the secondary control loop is designed based on the droop concept, which ensures that SOCs, reactive and active powers converge to their reference values, and on Multi-Agent System (MAS) theory to get a consensus among the reactive power and the State Of Charge (SOC) of the batteries in discharging mode. Moreover, it guarantees reliability and robustness with respect to any disconnection. The tuned system parameters are chosen in order to fit a three-time scale model (a time scale for each control objective: power converter control, droop control and consensus controls), which allows providing a large-signal stability analysis for the complete hybrid system based on HDS, MAS and singular perturbation theory.

Fixed-Time Nash Equilibrium Seeking in Time-Varying Networks

In this paper we introduce first-order and zeroth-order Nash equilibrium seeking dynamics with fixed-time convergence certificates for non-cooperative games having finitely many players. The first-order algorithms achieve exact convergence to the Nash equilibrium of the game in a finite time that can be additionally upper bounded by a constant that is independent of the initial conditions of the actions of the players. Moreover, these fixed-time bounds can be prescribed a priori by the system designer under an appropriate tuning of the parameters of the algorithms. When players have access only to measurements of their cost functions, we consider a class of distributed zeroth-order model-free adaptive dynamics that achieve semi-global practical fixed-time stability, qualitatively preserving the fixed-time bounds of the first-order dynamics. Moreover, by leveraging the property of fixed-time input-to-state stability, further results are obtained for mixed games where some of the players implement different seeking dynamics. Fast and slow switching communication graphs are also incorporated using tools from hybrid dynamical systems theory. We consider potential games as well as gener

A Framework for Decentralized Equilibrium Seeking in Networked Sampled-Data Games using Hybrid Control Tools*

We study the steady-state Nash equilibrium-seeking problem for sampled-data games with LTI dynamics and quadratic costs. The key challenge is to guarantee the robust stability and convergence properties of the closed-loop system in the presence of local individual sampling mechanisms assigned to each of the players in the game. This problem is non-trivial due to the unstable behaviors that can arise when sequential control updates (rather than parallel) emerge in the closed-loop system because of the existence of local control triggering mechanisms in each node of the network. To address this issue, we introduce a controls framework based on tools from hybrid dynamical systems theory. Our results are illustrated via numerical examples.

Hybrid Dynamical Control for Discharging Rate Consensus in AC-Bus Microgrids

In this work, a robust distributed hybrid algorithm is proposed for the primary and secondary control loops of an island AC-bus microgrid to provide large-signal stability of the complete system. A secondary control loop is designed from droop control and multi-agent systems theory to ensure that the State Of Charge (SOC) of the batteries in discharging mode converges to a consensus. Furthermore, this distributed strategy ensures robustness with respect to any plug-and-play event or communication failure. The DC-AC power converter of each battery in discharging mode is controlled in the primary loop by using hybrid dynamical system theory, which considers non-trivial issues in the model (switching and affine terms) and in the signals (constraints in the dwell time). A suited selection of gains allows using singular perturbation analysis to provide large-signal stability properties for the complete nonlinear model.

Accelerated Continuous-Time Approximate Dynamic Programming via Data-Assisted Hybrid Control

We introduce a new closed-loop architecture for the online solution of approximate optimal control problems in the context of continuous-time systems. Specifically, we introduce the first algorithm that incorporates dynamic momentum in actor-critic structures to control continuous-time dynamic plants with an affine structure in the input. By incorporating dynamic momentum in our algorithm, we are able to accelerate the convergence properties of the closed-loop system, achieving superior transient performance compared to traditional gradient-descent based techniques. In addition, by leveraging the existence of past recorded data with sufficiently rich information properties, we dispense with the persistence of excitation condition traditionally imposed on the regressors of the critic and the actor. Given that our continuous-time momentum-based dynamics also incorporate periodic discrete-time resets that emulate restarting techniques used in the machine learning literature, we leverage tools from hybrid dynamical systems theory to establish asymptotic stability properties for the closed-loop system. We illustrate our results with a numerical example.

Robust Hybrid Control for Demand Side Management in Islanded Microgrids

This paper focuses on designing a robust control law to manage the demand response of islanded microgrids composed of shifting and adjusting loads. On one side, Hybrid Dynamical System theory is suited here, because the microgrid model is composed of continuous-time dynamics (the energy stored in the battery and the adjustable loads), and discrete-time dynamics (the shifting loads). On the other side, Multi Agent System theory is used to control the adjusting loads in order to guarantee a consensus between them. Hence, non-uniform convergence of the State of Charge of the battery to a given reference is ensured. Robustness with respect to plug and play of any load and parameter variations is also ensured. Experimental results from a laboratory-scale microgrid validate the approach.

Control of Power Converters With Hybrid Affine Models and Pulse-Width Modulated Inputs

In this paper, hybrid dynamical systems theory is applied to the analysis and control of switched converters with Pulse-Width Modulated (PWM) inputs. The system is described by a state-space model with continuous flows and discrete jumps, without averaged equations. The modulation effects are captured in full without using time-dependent signals, by enlarging the state vector to include the PWM waveform generation process. Furthermore, the sample-and-hold mechanism associated with the sampling frequency is also taken into account with this approach. A control law is proposed based on a Lyapunov function candidate. Furthermore, convergence sets and the steady state jitter, inherent to PWM-based controllers, are analyzed estimating limit sets for the augmented state. Consequently, output chattering can be bounded. By using hybrid dynamical system theory, the control designer gains a deeper understanding of the effect of modulation in the closed-loop dynamics, avoiding the problems associated with the use averaged models. Experimental results validate the proposed method.

Hybrid Modelling and Control of a Class of Power Converters With Triangular-Carrier PWM Inputs

In this paper, a new control design procedure for a class of power converters based on hybrid dynamical systems theory is presented. The continuous-time dynamics, as voltage and current signals, and discrete-time dynamics, as the on- off state of the switches, are captured with a hybrid model. This model avoids the use of averaged and approximated models and includes the PWM as well as the sample-and-hold mechanism, commonly used in the industry. Then, another simplified hybrid system, whose trajectories match with the original one, is selected to design the controller and to analyse stability properties. Finally, an estimation of the chattering in steady state of the voltage and current signals is provided. The results are validated through simulation and experiments.

Hybrid dynamical control based on consensus algorithms for current sharing in DC-bus microgrids

The main objective of this work is to propose a novel paradigm for the design of two layers of control laws for DC-bus microgrids in islanded mode. An intensive attention will be paid to the inner control level for the regulation of DC–DC electronic power converters, where the use of Hybrid Dynamical System theory will be crucial to formulate and exploit switching control signals in view of reducing the dissipated energy and improving system performance. Indeed, this recent theory is well suited for analysing power electronic converters, since they combine continuous (voltage and currents) and discrete (on–off state of switches) signals avoiding, in this way, the use of averaged models. Likewise, an outer control level for controlling DC-bus microgrids will be developed to provide a distributed strategy that makes the microgrid scalable and robust with respect to blackouts of sources and/or loads, as well as, to provide a balance in the system of charge of the batteries, following the principle of Multi-Agent System theory. In this distributed strategy, they are several crucial and innovative aspects to be regarded such as the different converter architectures, the hybrid and nonlinear nature of these converters. Stability properties are guaranteed by using singular perturbation analysis.

A hybrid control strategy for quadratic boost converters with inductor currents estimation

This paper deals with a control strategy for a DC–DC quadratic boost converter. In particular, a hybrid control scheme is proposed to encompass a control law and an observer for the estimation of the system states, based only on the measurements of the input and output voltages. Differently from classical control methods, where the controller is designed from a small-signal model, here the real model of the system is examined without considering the average values of the discrete variables. Using hybrid dynamical system theory, asymptotic stability of a neighborhood of the equilibrium point is established, ensuring practical stability of the origin, which contains estimation and tracking errors. Experimental results show the effectiveness of the proposed approach.

Torque Coordination Control of Hybrid Electric Vehicles Based on Hybrid Dynamical System Theory

In order to reduce the vibration caused by mode switching of hybrid electric vehicles (HEVs) and achieve smooth mode switching, the hybrid input and output automation (HIOA) model of power control system of a parallel HEV is established based on the theory of hybrid dynamical system (HDS). Taking the switching from electric drive mode to hybrid drive mode for example, the torque coordination control is considered, and the performance is compared with the method without the torque coordination by using a rule-based control strategy. The simulation results in AVL Cruise show that, on the premise of ensuring the fuel economy and the emission, the mode switching process becomes smoother with smaller torque fluctuation and better driving comfort by considering the torque coordination.

Robust Ballistic Catching: A Hybrid System Stabilization Problem

This paper addresses a remaining gap between today's academic catching robots and their future in industrial applications: reliable task execution. A novel parameterization is derived to reduce the three-dimensional (3-D) catching problem to 1-D on the ballistic flight path. Vice versa, an efficient dynamical system formulation allows reconstruction of solutions from 1-D to 3-D. Hence, the body of the work in hybrid dynamical systems theory, in particular on the 1-D bouncing ball problem, becomes available for robotic catching. Uniform Zeno asymptotic stability from bouncing ball literature is adapted, as an example, and extended to fit the catching problem. A quantitative stability measure and the importance of the initial relative state between the object and end-effector are discussed. As a result, constrained dynamic optimization maximizes convergence speed while satisfying all kinematic and dynamic limits. Thus, for the first time, a quantitative success-oriented comparison of catching motions becomes available. The feasible and optimal solution is then validated on two symmetric robots autonomously playing throw and catch.

On the Practical Stability of Hybrid Control Algorithm With Minimum Dwell Time for a DC–AC Converter

This brief presents a control law based on a hybrid dynamical systems theory for a dc–ac converter. This theory is very suited for an analysis of power electronic converters, since it combines continuous (voltages and currents) and discrete (ON–OFF state of switches) signals avoiding, in this way, the use of averaged models. Here, practical stability results are induced for this tracking problem, ensuring a minimum dwell time associated with an Linear–Quadratic Regulator (LQR) performance level during the transient response and an admissible chattering around the operating point. The effectiveness of the resultant control law is validated by means of experiments.

Hybrid control scheme for a half-bridge inverter

This paper presents a control law based on Hybrid Dynamical Systems (HDS) theory for electronic inverters. This kind of systems are very suited for the use of such theory since they combine both kind of signals: continuous (voltages and currents) and discrete (on-off state of switches). Unlike previous applications of HDS to power converters, the studied problem can be considered as a tracking problem since the objective is to generate a desired ac voltage from a dc source. The effectiveness of the resultant control law is validated by means of simulations and experiments.

Multi-Section Hybrid Dynamical Scheduling of Flexible Manufacturing Systems

The use of hybrid dynamical systems theory opens a new horizon for flexible manufacturing systems scheduling. It even makes it possible to directly connect scheduling and MRP. In the present paper the most important new result is the proposed demand rates determination method for multi-section scheduling problems. Some other important achievements which makes possible the application of this approach are also discussed. These are, for example: •feedback control law resulting in stable (implementable with finite buffers) and regular (converging to periodic) processes •optimal demand rates determination for single-section problems

Allowable sampling period for consensus control of multiple general linear dynamical agents in random networks

This article studies the consensus problem for a group of sampled-data general linear dynamical agents over random communication networks. Dynamic output feedback protocols are applied to solve the consensus problem. When the sampling period is sufficiently small, it is shown that as long as the mean topology has globally reachable nodes, the mean square consensus can be achieved by selecting protocol parameters so that n − 1 specified subsystems are simultaneously stabilised. However, when the sampling period is comparatively large, it is revealed that differing from low-order integrator multi-agent systems the consensus problem may be unsolvable. By using the hybrid dynamical system theory, an allowable upper bound of sampling period is further proposed. Two approaches to designing protocols are also provided. Simulations are given to illustrate the validity of the proposed approaches.

Optimal Control of DC-DC Converter using Mixed Logical Dynamical System Model

This paper presents an optimal control method of dc-dc converters. The method is based on hybrid dynamical system theory. Specifically, the input of the considered system is confined to discrete value whereas the output to be controlled is continuous value. The system is modeled as a mixed logical dynamical system. Then, the optimal control law is obtained by means of model predictive control. The effectiveness of the proposed approach is illustrated through some numerical simulations.

Optimisation design of an energy management strategy for hybrid vehicles

This paper presents an innovative method to analyse and design an optimal energy management strategy for a power-split power train hybrid vehicle. A hybrid dynamical system theory is introduced to formulate the problem of hybrid vehicle control system design that incorporates both continuous and discrete dynamics. The sequential quadratic programming method is proposed to optimise power distribution. The dynamic programming method is employed to determine the vehicle operating mode transitions with optimal fuel efficiency and satisfactory drivability. An expert rule-based system and a fuzzy system are developed to implement the optimal strategies using the statistical method based on numerical solutions. The simulation results illustrate the effectiveness and applicability of the proposed design method.

Hybrid dynamical systems theory and the Signal language

The logic and synchronization characteristics of general dynamical systems called hybrid dynamical systems (HDS) are studied. The theory is related to discrete event dynamical system theory, but handles numerics as well as symbolics. It is supported by the programming language Signal and a mathematical model of general implicit dynamical systems. The core of the theory is the notion of HDS resolution which is based on a coding of any HDS into a dynamic graph which consists of a skew product of a polynomial dynamical system on the finite field of integers modulo 3 (to describe the transitions of the underlying automation) and directed graphs (to describe how data dependencies dynamically evolve). The resolution algorithms are based on the study of this dynamical system.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>