Hybrid System Theory Research Articles

Stability of short memory fractional-order hybrid systems

The stability theory of short memory fractional-order hybrid systems is studied in this article. Sufficient conditions of asymptotic stability and ultimately bounded stability for the nonlinear short memory fractional-order hybrid systems are proposed respectively. For the convenience of application, a convenient criterion of stability for the nonlinear short memory fractional-order hybrid systems is derived in the study. Demonstrative examples are given to verify the correctness of the proposed theorems in the part of simulation.

A hybrid approach to the stability analysis of sampled-data Lur’e systems

This work deals with the stability analysis of Lur’e systems under sampled-data control, where the Lur’e nonlinearity is assumed to be both sector and slope restricted. The stability conditions are derived by using a hybrid system representation and a generalized Lur’e type timer-dependent Lyapunov function. Considering a polynomial timer-dependence, the stability conditions are cast in sum-of-squares optimization problems aiming at computing the largest range of sampling intervals or the largest sector bounds on the nonlinearity for which the origin of the closed-loop system is globally asymptotically stable.

Generalized Functions in the Study of Signals and Systems

We collect three instances where the theory of generalized functions may still make contributions to the study of signals and systems. In the first, a purely algebraic approach is presented for LTI-ODE's, in terms of two operators, D and T, respectively the differentiation operator and the multiplication-by-the-independent-variable operator. This formalism adds simplicity, a duality theory, and nicely generalizes to other classes of operator equations and their solutions. In the second part we extend the classical bilateral Laplace transform to include Bohl functions with support in ℝ by invoking Sato's hyperfunctions. Finally, in the third case we use the Colombeau algebra to allow for products of generalized functions. This is important in the study of (smooth) nonlinear systems driven by impulsive inputs, and hybrid system theory.

A Hybrid Dynamical System Formulation of Capture-the-Flag Games

In this paper, we derive a comprehensive hybrid system representation for capture-the-fag games and a corresponding zero-sum game formulation. The hybrid system formulation and implementation is a first step towards the analysis and design of (sub)optimal control laws for the game. A scenario-based controller is employed to test the model in a simulation tool where the rules of the game are encoded.

Model-based event-triggered control for linear systems using a finite-time convergent observer

In this paper, we present an improved model-based event-triggered control approach for regulation of networked linear time-invariant plants by integrating a finite-time convergent observer. Utilizing the send-on-delta concept, we introduce two event-triggering strategies that substantially decrease the number of samples transmitted over the sensor-to-controller communication channel: (1) one strategy guarantees global asymptotic stability of a tunable compact neighborhood of the origin with a finite number of sampling events; (2) the other strategy ensures global asymptotic stability of the origin with arbitrarily large inter-sampling time. Through the lens of hybrid systems theory, we demonstrate that both methods avoid Zeno solutions, making them suitable for digital implementation, and both strategies exhibit robustness against both small and large perturbations. We showcase the advantages of our proposed strategies over other model-based approaches using a perturbed linearized batch reactor example.

Stability analysis of sampled-data control systems with input saturation: A hybrid system approach

This work addresses the stability analysis of sampled-data control systems subject to variable sampling intervals and input saturation. From a hybrid system representation, stability conditions based on quadratic timer-dependent Lyapunov functions are proposed. Considering affine and generic polynomial timer-dependence, these conditions are cast in semidefinite and sum-of-squares optimization problems to provide maximized estimates of the region of attraction or to provide a lower bound for the maximum allowable intersampling time considering a given set of admissible initial conditions.

Effective nonlinear Ehrenfest hybrid quantum-classical dynamics

The definition of a consistent evolution equation for statistical hybrid quantum-classical systems is still an open problem. In this paper, we analyze the case of Ehrenfest dynamics on systems defined by a probability density and identify the relations of the nonlinearity of the dynamics with the obstructions to define a consistent dynamics for the first quantum moment of the distribution. This first quantum moment represents the physical states as a family of classically-parametrized density matrices {hat{rho }}(xi ), for xi a classical point; and it is the most common representation of hybrid systems in the literature. Due to this obstruction, we consider higher order quantum moments, and argue that only a finite number of them are physically measurable. Because of this, we propose an effective solution for the hybrid dynamics problem based on approximating the distribution by those moments and representing the states by them.

Stability and Wardrop Equilibria of Noncooperative Routing With Time-Varying Load

Non-cooperative or selfish routing problems emerge in several applications of network control theory. Considering a multi-commodity setting subject to time-varying traffic demands, this paper studies the convergence properties of a family of non-cooperative routing control laws, originally developed in the literature for constant traffic demands. By employing results from hybrid systems theory and set stability, this paper identifies the minimum time between bounded load variations to assure the convergence of the controlled system towards a set of approximated Wardrop equilibria. Numerical simulations validate the results on a test scenario.

A μ‐H∞ control strategy for decreasing torque fluctuation of electro‐hydraulic integrated braking system in mode switching

AbstractDue to the difference of time‐domain response between hydraulic braking and regenerative braking, as well as changes of equivalent parameters and operating parameters during braking mode switching, it is liable to cause torque fluctuation, which affects braking safety and vehicle ride comfort. First, the uncertainties of vehicle load and frictional coefficient model are investigated. Second, the hybrid system theory is applied to provide state transfer condition for mode switching strategy. Finally, the control strategy that utilizes regenerative braking torque to compensate for difference of the required braking torque is designed, and a new μ‐H∞ control algorithm through D‐K iteration is presented to improve the robust performance. The proposed μ‐H∞ control strategy is examined under various braking situations, and the results indicate that (1) the μ‐H∞ controller have the advantage of robustness performance, the amplitude of regenerative braking is decreased by 6.14%, and the steady‐state error of hydraulic braking is decreased by 5.26% over the H∞, and (2) under the braking mode switching, the designed compensation control strategy has the performance of fast and accurate tracking of the desired torque, and the steady‐state error does not exceed 3.5%.

Stability analysis of sampled-data systems with sector-bounded input nonlinearity

This work proposes a method for the stability analysis of aperiodic sampled-data control systems with sector and slope bounded input nonlinearities. The stability conditions are derived by using a hybrid system representation and a timer-dependent Lur'e type Lyapunov function. Considering a polynomial timer-dependence, the stability conditions are cast in sum-of-squares optimization problems aiming at computing the largest range of sampling intervals or the largest sector bounds on the nonlinearity for which the origin of the closed-loop system is globally asymptotically stable.

Energy optimization for intelligent hybrid electric vehicles based on hybrid system approach in a car‐following process

AbstractConsidering the hybrid dynamical characteristics of multimode hybrid electric vehicle during a car‐following process, a novel energy management strategy based on hybrid system theory is proposed in this article. Firstly, nonlinear powertrain model and longitudinal dynamics of a single‐shaft parallel hybrid electric vehicle is built, and hybrid characteristics combined with continuous dynamics and discrete events during operating mode transition are described. Secondly, the nonlinear powertrain model and characteristics are approximated by the piecewise affine method, the mixed‐logic dynamic modeling method is introduced and system variables are defined. Then the hybrid dynamical model for multimode hybrid electric vehicle in a car‐following process is established with the hybrid system description language. Thirdly, according to the principle of receding horizon control, a hybrid model predictive controller is designed and applied for optimizing the multiobjective energy management problem in the car‐following process. Finally, the proposed control strategy is compared with a rule‐based control strategy, and the simulation results show that the proposed control strategy achieves fuel efficiency improvement while ensure the dynamic performance, driving safety and ride comfort during the car‐following process, and the designed controller meets the requirement of deep fusion of car‐following and energy management.

Controller Synthesis of Asynchronous Periodic Event-Triggered Networked Control Systems Subject to Quantization Effects

This paper aims at analyzing the input-to-state stability (ISS) of the networked control systems (NCSs) where the sensor-to-controller and the controller-to-actuator channels are equipped with different dynamic quantizers and event-triggering laws. In the scenarios of quantization effects and external disturbances, we propose to use an asynchronous periodic event-triggering mechanism (PETM) and an improved dynamic quantization scheme. The PETM has potential to reduce the network transmissions compared with the time-based one on the one hand, and is natural for the practical applications (e.g. the digital platforms) on the other hand. The asynchronous PETM, dynamic quantization effects and external disturbances are incorporated by a hybrid dynamical framework. With the help of a technique combining the hybrid system theory and a novel constructed Lyapunov function, the co-design problem of asynchronous periodic event-triggering conditions, dynamic output-feedback control and dynamic quantizer is firstly addressed thereby ensuring the ISS of the NCSs. Moreover, the proposed controller has an intuitive and explicit form, which can be solved easily. To assess the feasibility of the proposed method, a simulation is provided.

An online optimal energy management strategy for a dual-mode power-split hybrid electric vehicle based on hybrid MPC Algorithm*

This paper proposed a global on-line optimisation energy management strategy based on the hybrid model predictive control (HMPC) algorithm. First, the non-linear models of a dual-mode power-split hybrid electric vehicle is built. Then, the dual-mode power-split hybrid electric vehicle is considered as a hybrid system which includes continuous and discrete states, and a mixed logical dynamic (MLD) predictive model is built based on hybrid system theory. Thirdly, an HMPC energy management strategy is designed based on the MLD predictive model. The HMPC-based energy management strategy is compared with dynamic programming based and rule-based energy management strategies. The simulation results indicate that the HMPC-based energy management strategy is helpful for real-time control and improving fuel economy. good control performance. Finally, the control performance of the proposed HMPC-based energy management strategy is compared with that of the DP-based energy management strategy and rule- based energy management strategy. The simulation results indicated that the control performance of HMPC can achieve 80.6 % of that of DP.

Hybrid controller for global, robust, attitude stabilization of a magnetically actuated spacecraft

A novel approach to the three-axis attitude control of a magnetically actuated spacecraft is proposed, based on hybrid systems theory. Due to the actuators type, the system model is instantaneously underactuated and time-varying, so that low pointing errors and robustness are difficult to achieve at the same time. In this work, a uniting control design is developed, which combines a local H-inf regulator, with guaranteed performance, and a global nonlinear controller for ensuring global stability and robustness. Hybrid control theory is employed to develop a mixed continuous-discrete controller able to switch between different feedbacks. Controllers’ domains are designed according to appropriate input–output functions and to the magnitude of disturbances affecting the system. As a result, global attitude stability is ensured, while achieving local optimality and robustness against bounded disturbances, both matched and unmatched by the control action, and measurement noise. Analytical results are verified by means of realistic numerical simulations: the state errors comply with the computed bounds and stability is guaranteed for conservative assumptions on the magnitude of the unmatched disturbances.

Stable bilateral teleoperation with phase transition and haptic feedback

Abstract: In this paper, the bilateral teleoperation with haptic feedback is studied under the phase transition between the constraint and unconstraint motions. The stability of the teleoperation with both force feedback and phase transition is proven by Lyapunov–Krasovskii method and hybrid systems theory. The conditions of the theory results are more general than the others, they are time-varying delays, nonlinear systems, force feedback, and phase transition. By using the admittance control, the application results illustrate the efficiency of the proposed control method.

An Ergodic Measure for Active Learning From Equilibrium

This article develops KL-ergodic exploration from equilibrium (KL-E3), a method for robotic systems to integrate stability into actively generating informative measurements through ergodic exploration. Ergodic exploration enables robotic systems to indirectly sample from informative spatial distributions globally, avoiding local optima, and without the need to evaluate the derivatives of the distribution against the robot dynamics. Using a hybrid systems theory, we derive a controller that allows a robot to exploit equilibrium policies (i.e., policies that solve a task) while allowing the robot to explore and generate informative data using an ergodic measure that can extend to high-dimensional states. We show that our method is able to maintain Lyapunov attractiveness with respect to the equilibrium task while actively generating data for learning tasks such, as Bayesian optimization, model learning, and off-policy reinforcement learning. In each example, we show that our proposed method is capable of generating an informative distribution of data while synthesizing smooth control signals. We illustrate these examples using simulated systems and provide simplification of our method for real-time online learning in robotic systems. Note to Practitioners —Robotic systems need to adapt to sensor measurements and learn to exploit an understanding of the world around them such that they can truly begin to experiment in the real world. Standard learning methods do not have any restrictions on how the robot can explore and learn, making the robot dynamically volatile. Those that do are often too restrictive in terms of the stability of the robot, resulting in a lack of improved learning due to poor data collection. Applying our method would allow robotic systems to be able to adapt online without the need for human intervention. We show that considering both the dynamics of the robot and the statistics of where the robot has been, we are able to naturally encode where the robot needs to explore and collect measurements for efficient learning that is dynamically safe. With our method, we are able to effectively learn while being energetically efficient compared with state-of-the-art active learning methods. Our approach accomplishes such tasks in a single execution of the robotic system, i.e., the robot does not need human intervention to reset it. Future work will consider multiagent robotic systems that actively learn and explore in a team of collaborative robots.

Smooth Approximations for Hybrid Optimal Control Problems with Application to Robotic Walking

Abstract This paper investigates optimal control problems formulated over a class of hybrid dynamical systems which display event-triggered discrete jumps. Due to the discontinuous nature of the underlying dynamics, previous approaches to solving optimal control problems over this class of systems generally rely on fixing the number and sequence of discrete jumps a priori, or search over possible mode sequences in a combinatorial manner. Employing contributions from the geometric theory of hybrid systems, we instead formulate a family of smooth approximate problems formulated over a family of smooth control systems which faithfully approximate the dynamics of the original hybrid system, in an appropriate metric. Efficient gradient-based methods can be used to solve the smooth approximations, without specifying the sequence of discrete transitions ahead of time. Under appropriate hypothesis, the gradients of the smooth problem are shown to be well-conditioned and closely approximate the gradients of the non-smooth problem (when they exist). Two cases studies demonstrate the utility of the approach, including an in-depth application to generating a stable walking motion for a bipedal robot.

New trends in modeling and control of hybrid systems

New trends in modeling and control of hybrid systems

Fault Diagnosis of Lithium-Ion Battery Pack Based on Hybrid System and Dual Extended Kalman Filter Algorithm

For guaranteeing the performance and safety of battery systems, a valid fault diagnostic method is quite essential. This article presents a systematic fault diagnostic scheme based on a hybrid system for the typical faults of lithium-ion battery packs, including sensor faults and relay faults. The automata are established based on a hybrid system theory to simultaneously capture the continuous dynamics and discrete dynamics of the battery pack. The distributed diagnostic structure is adopted to avoid constructing the global model of the battery pack so that the computation burden can be reduced. A dual extended Kalman filter algorithm is developed to estimate the parameters, terminal voltages, and state of charges (SOC) of each cell in the battery pack. The current, terminal voltage residual, and SOC residual are used to implement the distinguishability analysis. The diagnostic scheme is implemented based on both the observation of the events and the distinguishability analysis of the continuous dynamics. The performance of the diagnostic method is validated for the battery pack that contains two batteries in series connection and two branches in parallel connection through the Federal Urban Driving Schedule driving cycle.

Discrete-Communication-Based Bipartite Tracking of Networked Robotic Systems via Hierarchical Hybrid Control

This paper investigates the bipartite tracking problem of networked robotic systems (NRSs) subject to input disturbances, discrete communications and signed directed graphs. Two new classes of hierarchical hybrid control algorithms (HHCAs), which involve both continuous and discontinuous signals in a uniform framework, are designed to solve the aforementioned problem in the model-independent control manner, i.e., without using the prior information of the system model. Besides, with the help of the Lyapunov statement and hybrid system theory, we establish several sufficient conditions for guaranteeing the convergence of the proposed hybrid algorithms. Finally, numerical examples are presented to illustrate the effectiveness of the proposed results.