Robust observer design by sign-stability for the monitoring of population systems

Monitoring problem in population ecology can be formalized as observer design for the population system in question: Supposing that we observe only certain species considered indicators, we want to recover or estimate the whole state process of the population system, where the state vector is usually composed from the biomasses of the single populations. In the present paper, for stably coexisting population systems, a new approach to the design of the corresponding observer system is proposed which, from the knowledge of the observed indicator(s), estimates the state process with exponential convergence. In the usual observer design, an auxiliary matrix, the so-called gain matrix must be found that guarantees the mentioned exponential convergence. The novelty is in that due to the required sign-stability (or qualitative stability) of the interaction pattern, the designed observer system (i.e. the gain matrix) is robust against quantitative changes in the inter- and intra-specific interactions. (Here the interaction pattern is described by a matrix having the signs as entries, indicating the quality of the interactions within and between the considered species.) In other words, under sign-stability conditions, in the observer design the same gain matrix can be used even if, due to environmental changes, the intensities of certain interactions suffer a quantitative change in the meanwhile. The requirement of sign-stability of the interaction pattern can be considered rather natural, since in a stably coexisting population system, it means for example that a predator–prey relation does not change into a prey–predator interaction, and interactions neither appear nor disappear within the system. Our approach to robust observer design is illustrated on model population systems, such as trophic chains of type resource-producer-primary consumer-secondary consumer and Lotka–Volterra system with vertical structure. For the latter system a Lyapunov function is also constructed that guarantees the global asymptotic stability of the positive equilibrium of the considered model.     

Consensus-based total-amount cooperative tracking control for multi-motor locomotive traction system

In locomotive traction system, unavoidable factors (such as idling and skidding) typically lead to the decline of traction performance of one or more motors, thereby resulting in the fluctuation of total torque traction amount. In this paper, the consensus-based total-amount cooperative tracking control (TACTC) is proposed to maintain the consensus of total torque traction amount with the given reference instruction. First, a disturbance observer is employed to estimate uncertain disturbances, then the output torque and observed values are fed back to design the total amount cooperative tracking control protocol, which is used to coordinate traction torque output redundancy of each individual motor. Simulation results show that the proposed approach is effective in reducing tracking time and tracking errors.     

Velocity observer design for the consensus in delayed robot networks

The consensus problem for networks of multiple agents consists in reaching an agreement between certain coordinates of interest using a distributed controller. It may be desirable that all the agents find a consensus at a given desired leader coordinate (Leader Follower Consensus Problem LFCP), or it may be only necessary that they agree at a certain coordinates value (Leaderless Consensus Problem LCP). Consensus has many practical applications in robot networks systems, where the interconnection of the agents may present variable time delays, hence rendering the stability analysis and control design more complex. Another problem that may arise is the possible lack of velocity measurements. In this work, a Proportional plus damping injection (P + d) controller together with a linear velocity observer is introduced. Our approach is able to solve both the LFCP and the LCP in networks of robots modeled as undirected weighted graphs with unknown asymmetric (bounded) variable time delays. Local (semi global) asymptotic stability is proven and simulation results are provided to test the performance of the proposed scheme.     

New approaches to positive observer design for discrete-time positive linear systems

This paper aims at providing new design approaches for positive observers of discrete-time positive linear systems based on a construction method of linear copositive Lyapunov function for positive systems. First, an efficient positive observer design approach is proposed by using linear programming such that the observer error system is exponentially stable. Furthermore, an interval observer design is proposed for uncertain positive systems. Then, the results are extended to positive time delay systems. In contrast with the previous design approaches, the new design method provides a general observer design with lower computational burden. Finally, three comparison examples are given to show the merit of the new design approach.     

Robust state-feedback control design for active suspension system with time-varying input delay and wheelbase preview information

This paper develops a robust state-feedback controller for active suspension system with time-varying input delay and wheelbase preview information in the presence of the parameter uncertainties. By employing system augmentation technique, a multi-objective control optimization model is first established and then this controller design is converted to a static full-state feedback controller design with robust H_∞ and generalized H₂ performance, wherein the model-dependent control gain is evaluated by transforming the related nonlinear matrix inequalities into their corresponding linear matrix inequality forms based on Lyapunov theory, and then LMI (Linear-Matrix-Inequality) technique is applied to solve and obtain the desired controller. A numerical simulation case is finally provided to reveal the effectiveness and advantages of the proposed controller.     

Impulsive observer design for a class of switched nonlinear systems with unknown inputs

This paper investigates hybrid observer design of a class of unknown input switched nonlinear systems. The distinguishing feature of the proposed method is that the stability of all subsystems of the error switched systems is not necessarily required. First, an output derivative-based method and time-varying coordinate transformation are considered to eliminate the unknown input. Then in order to maintain a satisfactory estimation performance, an impulsive full-order and switched reduced-order observer are developed with a pair of upper and lower dwell time bounds and constructing time-varying Lyapunov functions combined with convex combination technique. In addition, the time-varying Lyapunov functions method is also used to analyze the stability of a class of error switched nonlinear systems with stable subsystems. Finally, two examples are presented to demonstrate the effectiveness of the proposed method.     

Robust finite-time stabilizers for five-degree-of-freedom active magnetic bearing system

In this paper, the robust finite-time stabilization problem for a fully suspended five-degree-of-freedom active magnetic bearing system is addressed in the presence of external disturbances and additive uncertainties. By developing the nonsingular terminal sliding mode control and defining new nonlinear sliding surfaces, three separate classes of stabilizers are proposed to regulate and place the suspended rotor in the desired positions of air gaps within adjustable finite times. The suggested nonlinear sliding surfaces and designed control inputs for each class of stabilizers are two major differences between these stabilizers. It is mathematically proven that five control voltages of this system, designed by each class of the suggested stabilizers, are able to locate the suspended rotor at the centers of air gaps in the adjustable finite time which is summation of two reaching and settling finite times. Moreover, several new inequalities are extracted for determining the reaching and settling finite times related to the three classes of stabilizers. These inequalities reveal the dependencies between optional parameters of the proposed stabilizers and the mentioned finite times. Finally, numerical simulations are provided to illustrate the efficiency and good performance of each class of the designed stabilizers.     

Robust extended fractional Kalman filter for nonlinear fractional system with missing measurements

Accurate and effective state estimation is essential for nonlinear fractional system, since it can provide some vital operation information about the system. However, inevitably missing measurements and additive uncertainty in the gain will affect the performance of estimation result. Thus, in this paper, in order to deal with these problems, a novel robust extended fractional Kalman filter (REFKF) is developed for states estimation of nonlinear fractional system, by which the states can be estimated accurately even with missing measurements. Finally, simulation results are provided to demonstrate that the proposed method can achieve much better estimation performance than the conventional extended fractional Kalman filter (EFKF).     

Impulsive fixed-time observer for linear time-delay systems

This paper presents a fixed-time observer for a general class of linear time-delay systems. In contrast to many existing observers, which normally estimate system’s trajectory in an asymptotic fashion, the proposed observer estimates system’s state in a prescribed time. The proposed fixed-time observer is realized by updating the observer in an impulsive manner. Simulation results are also presented to illustrate the convergence behavior of the proposed fixed-time observer.     

Tracking controller design for random nonlinear benchmark system

This paper considers a benchmark system consisting of a rolling ball and a moving car in the oscillating surroundings. By using the Lagrange law, the dynamic model without disturbance is first constructed, then according to the relative motion principle, random oscillation of surroundings is transformed into the random noises in the constructed Lagrange equation. The special structure of the quasi-lower triangle of Lagrange equation motivates us to pay more attention to the vectorial backstepping technique. By selecting an appropriate Lyapunov-like function, a tracking controller with tunable parameters is designed such that all signals of the closed-loop system are bounded and track error can be made arbitrarily small.     

Composite fault-tolerant control with disturbance observer for stochastic systems with multiple disturbances

In this paper, a composite fault tolerant control (CFTC) with disturbance observer scheme is considered for a class of stochastic systems with faults and multiple disturbances. The disturbances are divided into two parts. One represents the stochastic disturbance with partial known information which is formulated by an exogenous system. The other is independent Wiener process. A stochastic disturbance observer is designed to estimate exogenous disturbance. To make the first type of disturbance can be rejected and the fault can be diagnosed, a composite fault diagnosis observer with disturbance observer is constructed. Furthermore, a composite fault-tolerant controller is proposed to compensate disturbances and faults. Finally, simulation examples are given to demonstrate the feasibility and effectiveness of the proposed scheme.     

Disturbance rejection for nonlinear systems with mismatched disturbances based on disturbance observer

A disturbance rejection approach based on disturbance observer is proposed for a class of nonlinear systems subject to mismatched disturbances. The mismatched disturbances are described by exogenous systems and satisfy partially-known information, which enter the system in the different channels with the control input. The disturbance observer is designed to estimate the mismatched disturbances, which can be introduced separately from the controller design. By integrating disturbance observer with back-stepping method, the disturbance observer plus back-stepping (DOPBS) controller can be constructed to reject the mismatched disturbances. And the asymptotically stability for the closed-loop system can be achieved. Finally, simulation examples are given to demonstrate the feasibility and effectiveness of the proposed scheme compared with existing methods.     

Anti-disturbance control based on disturbance observer for nonlinear systems with bounded disturbances

A composite anti-disturbance control problem for a class of nonlinear systems is studied in this paper. There are two types of disturbances in the systems, one is the matched disturbance with bounded variation rate, the other is the unmatched time-varying disturbances. A nonlinear disturbance observer is designed to estimate the matched disturbances, which can be presented separately from the controller design. By integrating DOBC with back-stepping method, a composite DOBC and back-stepping controller is proposed, and the disturbance estimations are introduced into the design of virtual control laws to compensate the unmatched disturbances. In addition, it is proved that all the states in the closed-loop system are uniformly ultimate bounded (UUB). Finally, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed method.     

Robust multivariable predictive control for laser-aided powder deposition processes

This paper presents a robust multivariable predictive control for laser-aided powder deposition (LAPD) processes in additive manufacturing. First, a novel control-oriented MIMO process model is derived. Then, the objective of achieving desired geometrical and thermal properties is formulated as one of generating and tracking nominal reference profiles of layer height and melting pool temperature. This is accomplished via a nonlinear model predictive control with guaranteed nominal stability. Furthermore, a local ancillary feedback law is derived to provide robustness to bounded uncertainties. The paper verifies the effectiveness of the proposed control via a case study on a laser cladding process.     

On convergence of the discrete-time nonlinear extended state observer

This paper concerns with the convergence of the discrete-time nonlinear extended state observer (ESO). Several kinds of discrete-time nonlinear ESO (NLESO) are proposed and then sufficient conditions based on linear matrix inequality (LMI) method are obtained to quantitatively reveal the relationship between the plant, the sampling interval, the parameter values of NLESO and its convergence. The theoretical results are verified by simulation using a motion control system. It shows that there may exist an optimal ω_o for a certain fixed sampling interval, and a smaller sampling interval generally generates better performance. What’s more, the proposed digital implementations of NLESO improve its performance over traditional Euler approximation discretization method.     

Robust self-triggered MPC with fast convergence for constrained linear systems

In this paper, a robust self-triggered model predictive control (MPC) scheme is proposed for linear discrete-time systems subject to additive disturbances, state and control constraints. To reduce the amount of computation on controller sides, MPC optimization problems are only solved at certain sampling instants which are determined by a novel self-triggering mechanism. The main idea of the self-triggering mechanism is to choose inter-sampling times by guaranteeing a fast decrease in optimal costs. It implies a fast convergence of system states to a compact set where it is ultimately bounded and a reduction of computation times to stabilize the system. Once the state enters a terminal region, the system can be stabilized to a robust invariant set by a state feedback controller. Robust constraint satisfaction is ensured by utilizing the worst-case set-valued predictions of future states in such a way that recursive feasibility is guaranteed for all possible realisations of disturbances. In the case where a priority is given to reducing communication costs rather than improvement in control performance in a neighborhood of the origin, a feedback control law based on nominal state predictions is designed in the terminal region to avoid frequent feedback. Performances of the closed-loop system are demonstrated by a simulation example.     

A novel performance criterion approach to optimum design of PID controller using cuckoo search algorithm for AVR system

This article presents a novel tuning design of Proportional-Integral-Derivative (PID) controller in the Automatic Voltage Regulator (AVR) system by using Cuckoo Search (CS) algorithm with a new time domain performance criterion. This performance criterion was chosen to minimize the maximum overshoot, rise time, settling time and steady state error of the terminal voltage. In order to compare CS with other evolutionary algorithms, the proposed objective function was used in Particle Swarm Optimization (PSO) and Artificial Bee Colony (ABC) algorithms for PID design of the AVR system. The performance of the proposed CS based PID controller was compared to the PID controllers tuned by the different evolutionary algorithms using various objective functions proposed in the literature. Dynamic response and a frequency response of the proposed CS based PID controller were examined in detail. Moreover, the disturbance rejection and robustness performance of the tuned controller against parametric uncertainties were obtained, separately. Energy consumptions of the proposed PID controller and the PID controllers tuned by the PSO and ABC algorithms were analyzed thoroughly. Extensive simulation results demonstrate that the CS based PID controller has better control performance in comparison with other PID controllers tuned by the PSO and ABC algorithms. Furthermore, the proposed objective function remarkably improves the PID tuning optimization technique.     

Mars entry guidance based on nonlinear model predictive control with disturbance observer

This paper investigates entry guidance of a capsule for pinpoint landing on Mars. In this scenario, the capsule is subject to the external disturbances caused by the atmosphere that can result in control saturation, and then undesired landing errors. To this end, a new guidance scheme to satisfy entry constraints, high-accuracy landing at high elevation sites, is proposed. The technical contributions of this work are two-fold: first, in order to mitigate the effects caused by large disturbance, a function describing the joint constraints of bank angle and slacked height is proposed; based on the nonlinear model predictive control (NMPC), a new algorithm is developed, where the constraints of dynamics, bank angle, slacked height, are sufficiently considered and precisely modeled; second, a state-space observer to improve the prediction of disturbance is introduced, which can significantly improve the accuracy of landing performance. The numerical simulations show the feasibility and validity of the proposed scheme.     

Robust state estimation for discrete time systems with colored noises and communication constraints

This paper investigates the state estimation problem for networked systems with colored noises and communication constraints. The colored noises are considered to be correlated to itself at other time steps, and communication constraints include two parts: (1) the information is quantized by a logarithmic quantizer before transmission, (2) only one node can access the network channel at each instant based on a specified media access protocol. A robust recursive estimator is designed under the condition of colored noises, quantization error and partially available measurements. The upper bound of the covariance of the estimation error is then derived and minimized by properly designing estimator gains. An illustrative example is finally given to demonstrate the effectiveness of the developed estimator.