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For electric bikes, this work develops linear parameter-varying (LPV) game-theoretic synthesis to regulate the trade-off between energy consumption per distance and propulsion capability in transience. Such a regulation plays like the transmission in transient state, compared to the gear transmission in steady state. Here, the propulsion dynamics is identified with LPV parameterisation that perfectly captures the non-linearity of the dynamics. Incorporation of this LPV plant with per-distance energy-motion performance forms a generalised plant with multiple L2-gain objectives. This generalised plant is specially constructed such that energy and motion objectives can share the same control and estimation storages without bringing conservatism to numerical solutions. Embedding the transient transmission into a dsPIC microcontroller, the authors simulate and experiment to credit such a LPV parameterisation and game-theoretic control for DC electric propulsion.

In this paper, the design problem of Gain‐Scheduled Output‐Feedback (GSOF) controllers using inexact scheduling parameters for morphing aircraft during the wing transition process is addressed. Both the stability of the closed‐loop system and the L2 gain performance can be guaranteed under the controller based on measured (not actual) scheduling parameters. Firstly, the linear parameter‐varying (LPV) model of morphing aircraft is established by Jacobian linearization and the additive uncertainty is introduced into the scheduling parameters. By employing non‐linear transformations, the problem is formulated as the solution to a set of parameter‐dependent linear matrix inequalities (LMI) with a single‐line search parameter. Finally, the robustness of the flight control system to the wing transition process is verified under the condition of both the uncertainty of aerodynamic parameters and of scheduling parameters.

The Hamilton–Jacobi–Issacs (HJI) inequality is the most basic relation in nonlinear H∞ design, to which no effective analytical solution is currently available. The sum of squares (SOS) method can numerically solve nonlinear problems that are not easy to solve analytically, but it still cannot solve HJI inequalities directly. In this paper, an HJI inequality suitable for SOS is firstly derived to solve the problem of nonconvex optimization. Then, the problems of SOS in nonlinear H∞ design are analyzed in detail. Finally, a two-step iterative design method for solving nonlinear H∞ control is presented. The first step is to design an adjustable nonlinear state feedback of the gain array of the system using SOS. The second step is to solve the L2 gain of the system; the optimization problem is solved by a graphical analytical method. In the iterative design, a diagonally dominant design idea is proposed to reduce the numerical error of SOS. The nonlinear H∞ control design of a polynomial system for large satellite attitude maneuvers is taken as our example. Simulation results show that the SOS method is comparable to the LMI method used for linear systems, and it is expected to find a broad range of applications in the analysis and design of nonlinear systems.

We address a unified convex combination approach to a class of switched uncertain nonlinear systems, focusing on quadratic stability and ℒ gain. In each subsystem, there are norm-bounded uncertainties in the system matrix and nonlinear terms with quadratic constraints. The proposed convex combination is original and unified in the sense of incorporating not only the nominal subsystem matrices but also uncertainty and quadratic constraints in the same form. When there is no single subsystem having the desired performance but a convex combination of subsystems does, we design a switching law so that the switched system achieves the same performance. Moreover, the discussion is extended to switching state feedback and its application to a boost converter.

Stability and L 2 -gain control for positive Takagi–Sugeno (T–S) fuzzy systems are further studied in this brief paper. First, considering that the system states are positive, some sufficient conditions of exponential asymptotic stability are obtained by applying a copositive Lyapunov function with membership-function-dependent (MFD) Lyapunov matrices. Based on a preset switching rule, the conditions are expressed as linear matrix inequalities by eliminating the nonconvex factors due to the time derivative of MFD Lyapunov matrices. Then, stability is extended to stabilization by designing a switching controller with time-varying controller gains such that the L 2 -gain performance requirements are satisfied. In addition, a quadratic switching strategy is established to further reduce conservativeness. Finally, the applicability and validity of the theoretical results are validated by two examples.

We present a novel approach that aims to address both safety and stability of a haptic teleoperation system within a framework of Haptic Shared Autonomy (HSA). We use Control Barrier Functions (CBFs) to generate the control input that follows the user’s input as closely as possible while guaranteeing safety. In the context of stability of the human-in-the-loop system, we limit the force feedback perceived by the user via a small L 2 -gain, which is achieved by limiting the control and the force feedback via a differential constraint. Specifically, with the property of HSA, we propose two pathways to design the control and the force feedback: Sequential Control Force (SCF) and Joint Control Force (JCF). Both designs can achieve safety and stability but with different responses to the user’s commands. We conducted experimental simulations to evaluate and investigate the properties of the designed methods. We also tested the proposed method on a physical quadrotor UAV and a haptic interface.

This paper investigates the problems of stability and L [in2}-gain for impulsive systems with time-delay. Inspired by the two-sided looped-functional method, a Lyapunov-like functional is established. Distinct from the previous researches, the information of the whole intervals x ( t k + ) to x ( t ) and x ( t ) to x ( t k +1 ) is completely exploited by the functional. Besides, a more advanced integral inequality is used and several integrals of the state are augmented, which are helpful to reduce the conservativeness. Based on the proposed method, sufficient criteria for stability and L 2 -gain are obtained. Numerical examples are provided to demonstrate the effect and the advantages of the proposed method.

This paper proposes a static anti-windup compensator (AWC) design methodology for the locally Lipschitz nonlinear systems, containing time-varying interval delays in input and output of the system in the presence of actuator saturation. Static AWC design is proposed for the systems by considering a delay-range-dependent methodology to consider less conservative delay bounds. The approach has been developed by utilizing an improved Lyapunov-Krasovskii functional, locally Lipschitz nonlinearity property, delay-interval, delay derivative upper bound, local sector condition, L 2 gain reduction from exogenous input to exogenous output, improved Wirtinger inequality, additive time-varying delays, and convex optimization algorithms to obtain convex conditions for AWC gain calculations. In contrast to the existing results, the present work considers both input and output delays for the AWC design (along with their combined additive effect) and deals with a more generic locally Lipschitz class of nonlinear systems. The effectiveness of the proposed methodology is demonstrated via simulations for a nonlinear DC servo motor system, possessing multiple time-delays, dynamic nonlinearity and actuator constraints.

This paper concerns the disturbance attenuation control problem for switched systems where the subsystems have different equilibria. By introducing a Lyapunov function that measures the proximity to the stability region, numerically testable stability and stabilization criteria of the systems are obtained. For multi-equilibrium switched systems with energy-bounded disturbances, the L 2 -gain is analyzed and the multi-equilibrium bound real lemma (ME-BRL) is derived. Further, an H ∞ multi-equilibrium switched ( H ∞ -MES) controller is designed, which ensures not only the nominal stability but also the H ∞ performance index of the closed-loop systems. Finally, the control method is applied to aero-engine control systems. The simulation results demonstrate that the proposed approach effectively attenuates the adverse impacts of external disturbances on the control systems.

H ∞ control is well-known for its robustness performance, but the spacecraft attitude H ∞ controller design under actuator misalignments and disturbances remains unexplored. In addition, the heavy computational demands prevent the implementation of an H ∞ controller for nonlinear systems in higher dimensions. To address these challenges, a robust H ∞ controller is proposed for the rigid spacecraft attitude control problem in the presence of actuator misalignments and disturbances based on the solution of the Hamilton–Jacobi–Isaacs (HJI) partial differential equation (PDE). The L 2 -gain of the closed-loop system is proved to be bounded by a specified disturbance attenuation level. An efficient sparse successive Chebyshev–Galerkin method is also proposed to solve the nonlinear HJI PDE, thus the implementation of the proposed controller is facilitated. It is also proved that the computational cost grows only polynomially with the system dimension. The effectiveness of the proposed robust H ∞ controller is validated through numerical simulations.