Data-driven hybrid switched-gain estimation for hybrid systems with periodic jumps.

In this paper, by applying interval methods, a new framework for analysis and control of discrete-time hybrid systems with parameter uncertainty is proposed. In analysis and control of hybrid systems, there are problem formulations such that convex polyhedra are computed, but for high-dimensional systems, it is difficult to solve these problems within the practical computation time. In this paper, instead of computing convex polyhedra, an interval method, which is one of classical methods in verified numerical computation, is applied to analysis and control of hybrid systems. By applying an interval method, discrete-time piecewise systems with parameter uncertainty can be approximately transformed into a mixed logical dynamical model.

Output regulation by error dynamic feedback in hybrid systems with periodic state jumps

It is well-known that the controls of neural network require that all the inputs of their input layer are available. Under this circumstance, the architecture of the neural network is constrained. Hence, this kind of neurocontrol cannot apply to a wide class of nonlinear and unknown dynamical systems, or the control system that requires more sensors. Although the unknown system state and the unknown system dynamics can be achieved from an adaptive observer and a learning neural network, respectively, the simultaneous existence of the estimated state error and the modeling error makes the control system more likely to be unstable. In this paper, a novel neurocontroller based on the concept of sliding mode with estimated state is constructed to tackle a wide class of unknown and nonlinear dynamical systems. The focal stability of the overall system can be verified by the Lyapunov stability criteria. Finally, simulations are presented to verify the usefulness of the proposed method.

Steady-state, harmonic response and moments of linear systems with periodic jumps

A survey of modeling and control of hybrid systems

Welcome to the proceedings of the 23rd ACM International Conference on Hybrid Systems: Computation and Control (HSCC 2020), held virtually for the first time. HSCC focuses on original research that involves concepts, tools, and techniques from computer science, control theory, and applied mathematics for the analysis and control of hybrid systems with an emphasis on computational aspects. Papers in HSCC range over a wide spectrum of topics from theoretical results to practical considerations, and from academic research to industrial adoption. Techniques presented at HSCC are applicable to both man-made cyber-physical systems and physical systems that naturally exhibit hybrid behavior.

The parallel ac and dc nature of most the distributed energy sources and loads, enforces the idea of forming hybrid ac/dc distributed generation (DG) systems. Such a hybrid structure demonstrates the main advantages of ac and dc distribution networks, such as easier renewable energy integration and less power conversion losses. A typical hybrid ac/dc DG system consists of: a dc-side, an ac-side and an interlinking voltage source inverter (VSI) as power interface between the two sides. Dc and ac resistive and constant power loads, as well dc and ac distributed energy resources (DERs) are incorporated. To enhance system reliability and dynamic performance, energy storage devices are connected to the dc link, allowing the power to flow in both directions, via a bidirectional boost converter. A challenging issue in the design of a hybrid ac/dc DG system is to apply effective, reliable and robust control in order to ensure stable operation at the desired conditions and to avoid adverse impacts between the different parts. In this frame, opposite to the small signal analysis, existing in the literature, in this paper, a nonlinear control design and analysis of the complete hybrid system is deployed. Based on the accurate system model, cascaded-mode proportional-integral (PI) controllers are designed and suitably implemented to the power electronic interfaces in order to regulate both the ac and dc voltages as well as the ac-side frequency. The stability analysis conducted on the nonlinear system model with the inner-loop current controllers involved, is based on advanced Lyapunov techniques and as proven in the paper guarantees closed-loop stability and convergence to the desired nonzero equilibrium. The entire hybrid system is simulated under DER and load rapid changes with the results to verify the smooth and robust behavior.

The Sixth International Symposium on Neural Networks (ISNN 2009)

In this article, we show that the existence of a Lyapunov–Krasovskii functional is necessary and sufficient condition for the uniform global asymptotic stability and the global exponential stability (GES) of time-invariant systems described by neutral functional differential equations in Hale's form. It is assumed that the difference operator is linear and strongly stable, and that the map on the right-hand side of the equation is Lipschitz on bounded sets. A link between GES and input-to-state stability is also provided.

This paper collects work on the analysis of hybrid systems. The hybrid systems considered are those that combine continuous dynamics (represented by differential or difference equations) with finite dynamics, usually thought of as being a finite automaton. We review multiple Lyapunov functions as a tool for analyzing Lyapunov of general hybrid systems. Background results, the author's introductory work, and subsequent extensions are covered. Specializing to hybrid systems with linear dynamics in each constituent mode and linear jump operators, we review some key theorems of Barabanov-Staroshilov (1988), and give corollaries encompassing several recently-derived stability by first approximation theorems in the literature. We also comment on the use of computational tests for of hybrid systems, and the general complexity. The result is a tutorial on the state of the art in theory and computation of hybrid systems stability.

This paper presents a hybrid system approach in the design of a singularityless task level controller. To achieve a singularityless motion control in the neighborhood of singularity, the hybrid system approach is used to integrate the task level controller and joint level controller. First, a hybrid system model is developed for the singularityless task level controller. A max-plus dynamic model is used to integrate the discrete switching control and continuous motion control in the controller. Based on this model, a smooth trajectory and control command for the hybrid system can be obtained. The Lyapunov theory was used to prove the stability of the singularityless controller. The new singularityless task level controller has been experimentally implemented and tested on a PUMA 560 robot manipulator. Experimental results have been employed to verify the theoretical conclusions, thus clearly demonstrating the advantages of the new task level control method.

Reliable, efficient, and affordable power supply system is a necessary tool for rapid socio-economic development of any country. Power supply in Nigeria is grossly inadequate and inefficient. This work presented a comparison analysis of Off-Grid Small hydro-Solar Photovoltaic-Diesel Generator hybrid system in three selected locations in South-west, Nigeria. The selected locations are Molete (Oyo state), Abeokuta (Ogun state) and Ede (Osun state). The hydro data for the three locations were collected from their respective River Basin Development Authorities, while the solar data were obtained from National Aeronautics and Space Administration’s global satellite database. The hybrid components consisting of Small hydropower (SHP), Solar Photovoltaic (PV), Battery (BB) and Diesel Generator (DG) were modelled and run using Hybrid Optimization Model for Electric Renewable software with the stream flow, the solar radiation, load and the system components costs as inputs. The work also carried out a comparative analysis based on economic parameters-return on investment and simple payback period different from the conventional use of net present cost, cost of energy(COE) and operating cost. The optimal hybrid combinations for these areas were compared with the usage of autonomous DG. The most optimal hybrid combination for Molete and Ede is PV-BB-SHP System with COEs of $0.347/kWh and $0.161/kWh respectively. The most optimal configuration for Abeokuta is PV-DG-BB-SHP with COE of $0.290/kWh. The results obtained (based on economic and technical considerations) showed that the hybrid system is viable for these areas. The outcome of the research will serve as guide for the government and prospective investors in formulating effective policies towards rapid development of renewable energy technologies in these areas.

This paper proposes an approach for the analysis and control of hybrid systems based on the hybrid automaton model. The problem that must be solved can be formulated as follows: given a hybrid automaton how can be restricted the regions associated with the controllable transition, in a systematic way, so that all the remaining behaviors satisfy certain properties. The hybrid nature of the manufacturing system is also investigated as a case study represented by a manufacturing cell. Throughout this paper the proposed methods are illustrated using an example taken from the manufacturing domain.

Hybrid system is a dynamic system that involves continuous, discrete behaviors, and the interactions between continuous physical components and discrete controllers. In this paper a hybrid modeling language (called HML) for hybrid systems is extended with templates to achieve code reuse. For the formal analysis of the corresponding hybrid system models in this modeling language, these models are translated into SMT (satisfiability modulo theories) formulas as the input to an SMT solver dReal which retains the capability of bounded reachability analysis for non-linear hybrid systems. Moreover, dReal can produce data for potential traces of hybrid systems, thus it can be employed to simulate on hybrid systems. In this paper the simulation and reachability analysis are integrated in a prototype tool (open source). We present a case study for an inverted pendulum with PID (Proportional-Integral-Derivative) controllers and a rod reactor system for temperature control, both are verified to demonstrate the efficiency of the prototype tool. We conclude that, this modeling language is capable of modeling and verification of hybrid systems based on simulation and bounded reachability analysis.

It is nontrivial to achieve exponential stability even for time-invariant nonlinear systems with matched uncertainties and persistent excitation (PE) condition. In this article, without the need for PE condition, we address the problem of global exponential stabilization of strict-feedback systems with mismatched uncertainties and unknown yet time-varying control gains. The resultant control, embedded with time-varying feedback gains, is capable of ensuring global exponential stability of parametric-strict-feedback systems in the absence of persistence of excitation. By using the enhanced Nussbaum function, the previous results are extended to more general nonlinear systems where the sign and magnitude of the time-varying control gain are unknown. In particular, the argument of the Nussbaum function is guaranteed to be always positive with the aid of nonlinear damping design, which is critical to perform a straightforward technical analysis of the boundedness of the Nussbaum function. Finally, the global exponential stability of parameter-varying strict-feedback systems, the boundedness of the control input and the update rate, and the asymptotic constancy of the parameter estimate are established. Numerical simulations are carried out to verify the effectiveness and benefits of the proposed methods.