Linear–quadratic switching control with switching cost

We study in this paper the linear–quadratic (LQ) optimal control problem of discrete-time switched systems with a constant switching cost for both finite and infinite time horizons. We reduce these problems into an auxiliary problem, which is an LQ optimal switching control problem with a cardinality constraint on the total number of switchings. Based on the solution structure derived from the dynamic programming (DP) procedure, we develop a lower bounding scheme by exploiting the monotonicity of the Riccati difference equation. Integrating such a lower bounding scheme into a branch and bound (BnB) framework, we offer an efficient numerical solution scheme for the LQ switching control problem with switching cost.     

Robust ℓ 1 performance analysis for linear systems with parametric uncertainties

In this contribution, a computational approach for analysing the robust ?_∞-gain (or the robust ?₁ performance) of uncertain linear systems is developed. In particular, the system's state-space matrices may have a rational dependence on structured parametric time-invariant or time-varying uncertainties. The computation is based on robust semi-definite programming and provides a trade-off between accuracy and computational effort. A novel matrix inequality condition to determine the star-norm of discrete-time systems is derived as an auxiliary result.     

Trajectory control of a two DOF rigid–flexible space robot by a virtual space vehicle

Model based control schemes use inverse dynamics of the robot arm to produce the main torque component necessary for trajectory tracking. For a model-based controller one is required to know the model parameters accurately. This is a very difficult job especially if the manipulator is flexible. This paper presents a control scheme for trajectory control of the tip of a two arm rigid–flexible space robot, with the help of a virtual space vehicle. The flexible link is modeled as an Euler–Bernoulli beam. The developed controller uses the inertial parameters of the base of the space robot only. Bond graph modeling is used to model the dynamics of the system and to devise the control strategy. The efficacy of the controller is shown through simulated and animation results.     

Dynamic output feedback control of a flexible air-breathing hypersonic vehicle via T–S fuzzy approach

By utilising Takagi–Sugeno (T–S) fuzzy set approach, this paper addresses the robust H_∞ dynamic output feedback control for the non-linear longitudinal model of flexible air-breathing hypersonic vehicles (FAHVs). The flight control of FAHVs is highly challenging due to the unique dynamic characteristics, and the intricate couplings between the engine and fight dynamics and external disturbance. Because of the dynamics’ enormous complexity, currently, only the longitudinal dynamics models of FAHVs have been used for controller design. In this work, T–S fuzzy modelling technique is utilised to approach the non-linear dynamics of FAHVs, then a fuzzy model is developed for the output tracking problem of FAHVs. The fuzzy model contains parameter uncertainties and disturbance, which can approach the non-linear dynamics of FAHVs more exactly. The flexible models of FAHVs are difficult to measure because of the complex dynamics and the strong couplings, thus a full-order dynamic output feedback controller is designed for the fuzzy model. A robust H_∞ controller is designed for the obtained closed-loop system. By utilising the Lyapunov functional approach, sufficient solvability conditions for such controllers are established in terms of linear matrix inequalities. Finally, the effectiveness of the proposed T–S fuzzy dynamic output feedback control method is demonstrated by numerical simulations.     

Distributed aggregative games for Euler–Lagrange systems with system parameter uncertainties

In this paper, an aggregative game of Euler–Lagrange (EL) systems is studied, where the parameters of the EL systems are not available. To seek the Nash equilibrium of the game, a novel distributed Nash equilibrium seeking algorithm is proposed, where the system parameters are not used in the feedback control. Moreover, a Lyapunov function is constructed such that EL players are proved to exponentially converge to the Nash equilibrium of the game. Finally, an example in the electricity market is provided to illustrate our result.     

Crew exploration vehicle (CEV) attitude control using a neural–immunology/memory network

This paper addresses the problem of the crew exploration vehicle (CEV) attitude control. CEVs are NASA's next-generation human spaceflight vehicles, and they use reaction control system (RCS) jet engines for attitude adjustment, which calls for control algorithms for firing the small propulsion engines mounted on vehicles. In this work, the resultant CEV dynamics combines both actuation and attitude dynamics. Therefore, it is highly nonlinear and even coupled with significant uncertainties. To cope with this situation, a neural–immunology/memory network is proposed. It is inspired by the human memory and immune systems. The control network does not rely on precise system dynamics information. Furthermore, the overall control scheme has a simple structure and demands much less computation as compared with most existing methods, making it attractive for real-time implementation. The effectiveness of this approach is also verified via simulation.     

Predefined-time control for Euler–Lagrange systems with model uncertainties and actuator faults

A novel adaptive predefined-time tracking control algorithm is proposed for the Euler–Lagrange systems (ELSs) with model uncertainties and actuator faults. Compared with traditional finite-time and fixed-time studies, the system output tracking error under the proposed predefined-time controller converges to a small neighborhood of zero in finite time, whose upper bound is exactly a design parameter in the control algorithm. For the uncertain model, radial-based function neural network (RBFNN) is utilized to approximate the continuous uncertain dynamics. To deal with the actuator faults, an adaptive control law is involved in the fault-tolerant controller. In order to achieve the predefined-time bounded, a novel predefined-time sliding mode surface is designed. It is proved that the tracking error vector trajectory of closed-loop system is semi-globally uniformly ultimately predefined-time bounded, and the upper bounds of both the system settling time and the corresponding output tracking error can be adjusted with a simple parameter. Simulation examples finally demonstrate the effectiveness of the proposed control algorithm.     

Multi-objective H ∞ control for vehicle active suspension systems with random actuator delay

This article is concerned with the problem of multi-objective H _∞ control for vehicle active suspension systems with random actuator delay, which can be represented by signal probability distribution. First, the dynamical equations of a quarter-car suspension model are established for the control design purpose. Secondly, when taking into account vehicle performance requirements, namely, ride comfort, suspension deflection and the probability distributed actuator delay, we present the corresponding dynamic system, which will be transformed to the stochastic system for the problem of multi-objective H _∞ controller design. Third, based on the stochastic stability theory, the state feedback controller is proposed to render that the closed-loop system is exponentially stable in mean-square while simultaneously satisfying H _∞ performance and the output constraint requirement. The presented condition is expressed in the form of convex optimisation problems so that it can be efficiently solved via standard numerical software. Finally, a practical design example is given to demonstrate the effectiveness of the proposed method.     

An H∞ suboptimal robust control approach for systems with uncertainties and data dropouts

This paper studies the design of control systems subject to plant uncertainties and data losses in the channel connecting the plant sensor with the controller. The controller design has two main objectives. The first one is to robustify the control law against plant uncertainties. The other one is to achieve good performance by minimising the variance of the error signal. Data losses are modelled as an independent and identically distributed sequence of Bernoulli random variables. For analysis and design, this random variable is replaced by an additive noise plus gain channel model. To cope with structural uncertainties in the model of the plant, an H_∞ control technique is employed. The controller is synthesised in order to make the closed-loop system robust against structural uncertainties of the nominal model, while achieving optimal performance of the system in the presence of dropouts.     

Quadratic and H∞ switching control for discrete-time linear systems with multiplicative noises

The goal of this paper is to study the switched stochastic control problem of discrete-time linear systems with multiplicative noises. We consider both the quadratic and the H_∞ criteria for the performance evaluation. Initially we present a sufficient condition based on some Lyapunov–Metzler inequalities to guarantee the stochastic stability of the switching system. Moreover, we derive a sufficient condition for obtaining a Metzler matrix that will satisfy the Lyapunov–Metzler inequalities by directly solving a set of linear matrix inequalities, and not bilinear matrix inequalities as usual in the literature of switched systems. We believe that this result is an interesting contribution on its own. In the sequel we present sufficient conditions, again based on Lyapunov–Metzler inequalities, to obtain the state feedback gains and the switching rule so that the closed loop system is stochastically stable and the quadratic and H_∞ performance costs are bounded above by a constant value. These results are illustrated with some numerical examples.     

An approximation-based load-balancing algorithm with admission control for cluster web servers with dynamic workloads

The growth of web-based applications in business and e-commerce is building up demands for high performance web servers for better throughputs and lower user-perceived latency. These demands are leading to a widespread substitution of powerful single servers by robust newcomers, cluster web servers, in many enterprise companies. In this respect the load-balancing algorithms play an important role in boosting the performance of cluster servers. The previous load-balancing algorithms which were designed for the handling of static contents in web services suffer from significant performance degradation under dynamic and database-driven workloads. Regarding this, we propose an approximation-based load-balancing algorithm with admission control for cluster-based web servers in this study. Since it is difficult to accurately determine the loads of web servers through feedbacks from distributed agents in web servers, we propose an analytical model of a web server to estimate the web servers’ loads. To achieve this, the algorithm classifies requests based on their service times and track numbers of outstanding requests for each class of each web server node and also based on their resource demands to dynamically estimate the loads of each node. For the error handling of the model a proportional integral (PI) controller from control theory is used. Then the estimated available capacity of each web server is used for load balancing and admission control decisions. The implementation results with a standard benchmark confirm the effectiveness of the proposed scheme, which improves both the mean response time and the throughput of the cluster compared to rival load-balancing algorithms, and also avoids situations in which the cluster is overloaded, even when the request rates are beyond the cluster capacity.     

The bounded energy optimal control for a class of distributed parameter systems†

The bounded energy optimal control for one-dimensional linear stationary distributed parameter system is solved here. The criterion function is a quadratic functional of the output.

Obtaining the optimal control involves the computation of the solution of a certain non-linear integral equation. The method of solving this integral equation is approximating the kernel of the integral operator by a sequence of degenerate kernels. It is shown that the sequence of approximate solutions of the approximate integral equations converges to the optimal solution; and that the sequence of approximate values of the criterion, converges to the optimal value of the criterion.     

Driver–vehicle cooperation: a hierarchical cooperative control architecture for automated driving systems

The concept of automated driving changes the way humans interact with their cars. However, how humans should interact with automated driving systems remains an open question. Cooperation between a driver and an automated driving system—they exert control jointly to facilitate a common driving task for each other—is expected to be a promising interaction paradigm that can address human factors issues caused by driving automation. Nevertheless, the complex nature of automated driving functions makes it very challenging to apply the state-of-the-art frameworks of driver–vehicle cooperation to automated driving systems. To meet this challenge, we propose a hierarchical cooperative control architecture which is derived from the existing architectures of automated driving systems. Throughout this architecture, we discuss how to adapt system functions to realize different forms of cooperation in the framework of driver–vehicle cooperation. We also provide a case study to illustrate the use of this architecture in the design of a cooperative control system for automated driving. By examining the concepts behind this architecture, we highlight that the correspondence between several concepts of planning and control originated from the fields of robotics and automation and the ergonomic frameworks of human cognition and control offers a new opportunity for designing driver–vehicle cooperation.