Mixed H∞ and passive control for a class of nonlinear switched systems with average dwell time via hybrid control approach

This paper investigates the mixed H_∞ and passive control problem for a class of nonlinear switched systems based on a hybrid control strategy. To solve this problem, firstly, using the Takagi–Sugeno (T–S) fuzzy model to approximate every nonlinear subsystem, the nonlinear switched systems are modeled as the switched T–S fuzzy systems. Secondly, the hybrid controllers are used to stabilize the switched T–S fuzzy systems. The hybrid controllers consist of dynamic output-feedback controllers for every subsystem and state updating controllers at the switching instant. Thirdly, a new performance index is proposed for switched systems. This new performance index can be viewed as the mixed weighted H_∞ and passivity performance. Based on this new performance index, the weighted H_∞ control problem and the passive control problem for switched T–S fuzzy systems via the hybrid control strategy are solved in a unified framework. Together the multiple Lyapunov functions (MLFs) approach with the average dwell time (ADT) technique, new design conditions for the hybrid controllers are obtained. Under these conditions, the closed-loop switched T–S fuzzy systems are globally uniformly asymptotically stable with a prescribed mixed H_∞ and passivity performance index. Moreover, the desired hybrid controllers can be constructed by solving a set of linear matrix inequalities (LMIs). Finally, the effectiveness of the obtained results is illustrated by a numerical example.     

Virtual camera-based visual servoing for rotorcraft using monocular camera and gyroscopic feedback

In this paper, an image-based visual servoing (IBVS) control strategy with a virtual camera frame is proposed for multirotor vehicles. Compared to previous works, the proposed IBVS controller requires minimal sensors in the position loop: a monocular camera and gyroscope. To achieve this, the visual feature projected onto the virtual image plane is associated with the plane’s normal instead of relying on an additional attitude estimator and prior knowledge of the plane’s inclination. Furthermore, we show that the ratio velocity, when scaled by the image moment, exhibits a similar dynamics to the linear velocity. The finding allows the quantity to be recovered and used for control with a monocular camera without other metric cues. To provide feedback for the controller, an Extended Kalman filter for estimating the ratio velocity, target plane’s inclination, and relative rotation between the current and reference camera frame is developed using only monocular vision and gyroscopic measurements. To validate the proposed controller and estimation strategy, both simulation and real-world flight experiments were carried out. The quadrotor smoothly and robustly tracked both dynamic horizontal and static inclined targets, without prior knowledge of the target’s inclination. Overall, the proposed regime offers a lightweight and robust alternative IBVS solution for rotorcraft.     

Simultaneous H∞ stabilization for large-scale systems within distributed wireless networked control framework over fading channels

In this paper, the simultaneous H_∞ stabilization problem is investigated for a physically interconnected large-scale system which works in multiple operation modes. A distributed wireless networked control framework is introduced, in which the distributed dynamic output feedback controllers not only use the local measurements, but also receive the neighboring controllers’ broadcasts via wireless networks. The channel fading in wireless communications is described as the Rice fading model. Our focus is on the design of the distributed controllers such that the large-scale system is mean-square stable in each operation mode and achieves a prescribed H_∞ disturbance attenuation level. By employing the Lyapunov functional method and related stochastic analysis techniques, a sufficient condition on the existence of desired controllers is presented, and the parameterization of the controller gains is derived. Finally, a numerical example is utilized to illustrate the feasibility of the proposed scheme.     

Direct data-driven design of LPV controllers with soft performance specifications

If only experimental measurements are available, direct data-driven control design becomes an appealing approach, as control performance is directly optimized based on the collected samples. The direct synthesis of a feedback controller from input-output data typically requires the blind choice of a reference model, that dictates the desired closed-loop behavior. In this paper, we propose a data-driven design scheme for linear parameter-varying (LPV) systems to account for soft performance specifications. Within this framework, the reference model is treated as an additional hyper-parameter to be learned from data, while the user is asked to provide only indicative performance constraints. The effectiveness of the proposed approach is demonstrated on a benchmark simulation case study, showing the improvement achieved by allowing for a flexible reference model.     

Delay-dependent dissipative control for linear time-delay systems

This paper deals with the problem of delay-dependent dissipative control for a class of linear time-delay systems. We develop the design methods of dissipative static state feedback and dynamic output feedback controllers such that the closed-loop system is quadratically stable and strictly (Q,S,R)-dissipative. Sufficient conditions for the existence of the quadratic dissipative controllers are obtained by using linear matrix inequality (LMI) approach. Furthermore, a procedure of constructing such controllers from the solutions of LMIs is given. It is shown that the solvability of a dissipative controller design problem is implied by the feasibility of LMIs. The main results of this paper unify the existing results on H^∞ control and passive control.     

Generic two-degree-of-freedom linear and fuzzy controllers for integral processes

This paper presents a new framework for the design of generic two-degree-of-freedom (2-DOF), linear and fuzzy, controllers dedicated to a class of integral processes specific to servo systems. The first part of the paper presents four 2-DOF linear PI controller structures that are designed using the Extended Symmetrical Optimum method to ensure the desired overshoot and settling time. The second part of the paper presents an original design method for 2-DOF Takagi-Sugeno PI-fuzzy controllers based on the stability analysis theorem. Experimental results for the speed control of a servo system with variable load illustrate the performance of the new generic control structures.     

Robust Visual Servoing of Robot Manipulators with Neuro Compensation

This paper considers the problem of visual servoing of planar robot manipulators in the presence of uncertainty associated with robot dynamics, camera system and Jacobian matrix. By using radial basis function neural networks, these uncertainties can be compensated effectively. Two kinds of robust visual servoing are proposed, one is for image uncertainties, another is for Jacobian matrix uncertainty. By Lyapunov method and input-to-state stability technique, we prove that these robust controllers with neural compensators are stable. Real-time experiments are presented to show the applicability of the approach presented in this paper.     

Stability and L1-gain analysis for switched positive T–S fuzzy systems under asynchronous switching

This paper is concerned with the exponential stability and L₁-gain analysis problem for switched positive T–S fuzzy systems under both time-varying delays and asynchronous switching. By permitting the increase of the designed multiple Lyapunov functionals during the running time of the activated subsystem, solvable conditions for the stability and L₁-gain are developed by adopting the mode-dependent average dwell time (MDADT) technique. The desired controllers guaranteeing the stability and the L₁-gain performance are designed based on the obtained solvable conditions. An example is given to demonstrate the effectiveness of the proposed methods.     

A switched system approach to H∞ control of networked control systems with time-varying delays

This paper is concerned with the H_∞ control problem for a class of networked control systems (NCSs) with time-varying delay that is less than one sampling period. By applying a new working mode of the actuator and considering state feedback controllers, a new discrete-time switched system model is proposed to describe the NCS. Based on the obtained switched system model, a sufficient condition is derived for the closed-loop NCS to be exponentially stable and ensure a prescribed H_∞ performance level. The obtained condition establishes relations among the delay length, the delay variation frequency, and the system performances of the closed-loop NCS. Moreover, a convex optimization problem is formulated to design the H_∞ controllers which minimize the H_∞ performance level. An illustrative example is given to show the effectiveness of the proposed results.     

Reliable H∞ control on saturated linear Markov jump system with uncertain transition rates and asynchronous jumped actuator failure

This paper is concerned with reliable H_∞?control for saturated linear Markov jump systems with uncertain transition rates and asynchronous jumped actuator failure. The actuator failures are assumed to occur randomly under the Markov process with a different jumping mode from the system jumping mode. In considering the mixed-mode-dependent state feedback controller, both H_∞ stochastic stability analysis for closed-loop system with completely accessible transition rates and uncertain transition rates are investigated. Moreover, based on the obtained stability conditions, the H_∞?control problems are investigated, and the controller gains can be obtained by solving a convex optimization problem with minimizing H_∞ performance as objective and linear matrix inequalities (LMIs) as constraints. The problem of designing state feedback controllers such that the estimate of the domain of attraction is enlarged is also formulated and solved as an optimization problem with LMI constraints. Simulation results are presented to illustrate the effectiveness of the proposed results.     

PI consensus error transformation for adaptive cooperative control of nonlinear multi-agent systems

A solution is provided in this paper for the adaptive approximate consensus problem of nonlinear multi-agent systems with unknown and non-identical control directions assuming an underlying graph topology having a spanning tree. This is achieved with the introduction of a novel variable transformation called PI consensus error transformation. The new variables include the position error of each agent from some reference trajectory chosen by him, which represents the agent’s selection for the desired swarm trajectory, along with an integral term of the weighted total displacement of the agent’s position from all neighbor positions. It is proven that if these new variables are bounded and regulated to zero, then asymptotic approximate consensus among all agents is ensured. Using classical Nussbaum gain based techniques, distributed controllers are designed to regulate the PI consensus error variables to zero and ultimately solve the approximate agreement problem. The proposed approach also allows for a specific calculation of the final consensus trajectory based on the controller parameter selection and the associated graph topology. It is shown that all agent positions converge towards a neighborhood of the weighted average of all agents reference trajectories. Simulation results verify our theoretical derivations.     

Flocking motion in swarms with limited sensing radius and heterogeneous input constraints

This paper addresses the flocking motion problem for swarms of agents with two restrictions: limited communication/detection ranges and different input constraints. In this problem, the distance between pairs of agents determines if a communication/detection link exists among them, while each agent has a different control action bound. We use the notion of proximity graph to model communication/detection between agents and provide distributed controllers designed for leaderless and leader-followers flocking motion scenarios. Our proposed designs preserve the connectivity of the proximity graph while the control effort satisfies the bound of each particular agent. Unlike previous results, our protocols take advantage of the group’s input heterogeneity to use agents with a greater capacity to compensate for neighbors that are less capable of meeting the group’s requirements. Additionally, our designs are based only on local state errors and are robust to non-modeled edge failures. To illustrate the effectiveness of our proposal, we use numerical simulations of different flocking scenarios.     

Finite-time H∞ control for a class of discrete-time nonlinear singular systems

This paper investigates the finite-time control problems for a class of discrete-time nonlinear singular systems via state undecomposed method. Firstly, the finite-time stabilization problem is discussed for the system under state feedback, and a finite-time stabilization controller is obtained. Then, based on which, the finite-time H_∞ boundedness problem is studied for the system with exogenous disturbances. Finally, an example of population distribution model is presented to illustrate the validity of the proposed controller. Because there is no any constraint for singular matrix E in the paper, controllers can be designed for more discrete-time nonlinear singular systems.     

Backstepping design for controlling electrohydraulic servos

The backstepping technique is one of the tools which provides control Lyapunov functions (CLFs) and, therefore, control laws for automatic systems. In this paper, the backstepping design for position and force nonlinear electrohydraulic servos is investigated. Three control laws ensuring the asymptotic stability of references tracking are obtained by constructing CLFs on the errors concerning the state variables and theirs desired values. The possibility of converting a position servo into a force servo, with only minimal hard modification, is proved. An approach based on partitioning the state system into two subsystems—a first one stable, and a second one taken as framework of control synthesis by backstepping technique—was developed and used. Using as reference point a flight controls hydromechanical servo, numerical simulations were reported from viewpoint of servo time constant performance. Certain conjectures, concerning the behaviour of systems mathematical models, in connection with mathematical methodologies of control synthesis operating on them, are finally stressed.     

Single landmark feedback-based time optimal navigation for a differential drive robot

In this paper, we propose a feedback-based control approach to execute the time optimal motion trajectories for a differential drive robot. These trajectories are composed of straight lines and rotations in place. We show that the evolution of the position of a single landmark over time, in a local reference frame, makes it possible to track a prescribed time-optimal robot’s trajectory, based on feedback of the landmark’s position. We also show that the closed-loop system is an exponentially stable one with a nonvanishing perturbation, and that globally uniformly ultimately boundedness of the tracking errors can be achieved. The two main results of this work are: 1) Our approach leverages visual servo control type of methods with tools from optimal control for executing time-optimal trajectories in the state space based on feedback information. 2) The approach is able to work with the minimum number of landmarks–only one–this represents a necessary and sufficientcondition for landmark-based navigation. Experiments in a physical robot, a nonholonomic differential drive system equipped with an omnidirectional laser sensor, are shown, which validate the proposed theoretical modelling.     

Robust sliding mode control of a DC/DC Boost converter with switching frequency regulation

This paper presents the design of a hysteresis band controller to regulate the switching frequency in a sliding mode controlled nonlinear Boost power converter. The proposed architecture relies on a piecewise linear modeling of the switching function behavior within the hysteresis band, and consists of a continuous-time integral-type controller that modifies the amplitude of the hysteresis band of the comparator in accordance with the error between the desired and the actually measured switching period. The study provides the dynamical models of the converter operating in sliding mode and the switching frequency control loop. Moreover, the design of the parameters of both the sliding mode control and the switching frequency controller guarantee the fulfilment of the desired output voltage regulation of the Boost converter and the steady state setting of the switching frequency with a known, taylored dynamics. A Boost power converter prototype has been built to validate the proposal. Experimental results confirm the predicted good performance of the controllers, as well as the robustness with respect to changes in the switching frequency reference and the system parameters.     

Event-triggered control for active vehicle suspension systems with network-induced delays

This paper presents a novel event-triggered H_∞ static output-feedback control for active vehicle suspension systems with network-induced delays. The proposed control schema introduces an event-triggering mechanism in the suspension system such that the communication resources can be significantly saved. By applying some improved slack inequalities and an augmented Lyapunov–Krasovskii functional (LKF), a new design condition expressed in the form of linear matrix inequalities (LMIs) is developed to derive the desired event-triggered controller. The obtained algorithm is then employed to solve the static output-feedback control gain. Compared with the traditional sampled-data H_∞ control scheme, the proposed controller is able to provide an enhanced disturbance attenuation level while saving the control cost. Finally, comparative simulation results are provided to show the performance of the proposed event-triggered controller.     

Modelling and optimal control of a time-delayed switched system in fed-batch process

The main control goal of the fed-batch process is to maximize the yield of target product as well as to minimize the operation costs simultaneously. Considering the existence of time delay and the switching nature in the fed-batch process, a time-delayed switched system is proposed to formulate the 1,3-propanediol (1,3-PD) production process. Some important properties of the system are also discussed. Taking the switching instants and the terminal time as the control variables, a free terminal time delayed optimal control problem is then presented. Using a time-scaling transformation and parameterizing the switching instants into new parameters, an equivalently optimal control problem is investigated. A numerical solution method is developed to seek the optimal control strategy by the smoothing approximation method and the gradient of the cost functional together with that of the constraints. Numerical results show that the mass of target product per unit time at the terminal time is increased considerably.     

Design and comparison of LQG/LTR and H∞ controllers for a VSTOL flight control system

In this paper two robust controllers for a multivariable vertical short take-off and landing (VSTOL) aircraft system are designed and compared. The aim of these controllers is to achieve robust stability margins and good performance in step response of the system. LQG/LTR method is a systematic design approach based on shaping and recovering open-loop singular values while mixed-sensitivity H_∞ method is established by defining appropriate weighting functions to achieve good performance and robustness. Comparison of the two controllers show that LQG method requires rate feedback to increase damping of closed-loop system, while H_∞ controller by only proper choose the weighting functions, meets the same performance for step response. Output robustness of both controllers is good but H_∞ controller has poor input stability margin. The net controller order of H_∞ is higher than the LQG/LTR method and the control effort of them is in the acceptable range.