Observer-based State Feedback Controller Research Articles

Observer-based control for plasma glucose regulation in type 1 diabetes mellitus patients with unknown input delay.

This article introduces an observer-based control strategy tailored for regulating plasma glucose in type 1 diabetes mellitus patients, addressing challenges like unknown time-varying delays and meal disturbances. This control strategy is based on an extended Bergman minimal model, a nonlinear glucose-insulin model to encompass unknown inputs, such as unplanned meals, exercise disturbances, or delays. The primary contribution lies in the design of an observer-based state feedback control in the presence of unknown long delays, which seeks to support and enhance the performance of the traditional artificial pancreas by considering realistic scenarios. The observer and control gains for the observer-based control are computed through linear matrix inequalities formulated from Lyapunov conditions that guarantee closed-loop stability. This design deploys a soft and gentle dynamic response, similar to a natural pancreas, despite meal disturbances and input delays. Numerical tests demonstrate the scheme's effectiveness in glycemic level regulation and hypoglycemic episode avoidance.

Combined Observer-Based State Feedback and Optimized P/PI Control for a Robust Operation of Quadrotors

This paper deals with a discrete-time observer-based state feedback control design by taking into consideration bounded parameter uncertainty, actuator faults, and stochastic noise in an inner control loop which is extended in a cascaded manner by outer PI- and P-control loops for velocity and position regulation. The aim of the corresponding subdivision of the quadrotor model is the treatment of the control design in a systematic manner. In the inner loop, linear matrix inequality techniques are employed for the placement of poles into a desired area within the complex z-plane. A robustification of the design towards noise is achieved by optimizing both control and observer gains simultaneously guaranteeing stability in a predefined bounded state domain. This procedure helps to reduce the sensitivity of the inner control loop towards changes induced by the outer one. Finally, a model-based optimization process is employed to tune the parameters of the outer P/PI controllers. To allow for the validation of accurate trajectory tracking, a comparison of the novel approach with the use of a standard extended Kalman filter-based linear-quadratic regulator synthesis is presented to demonstrate the superiority of the new design.

Finite-Time H∞ Controllers Design for Stochastic Time-Delay Markovian Jump Systems with Partly Unknown Transition Probabilities.

This paper concentrates on the finite-time H∞ control problem for a type of stochastic discrete-time Markovian jump systems, characterized by time-delay and partly unknown transition probabilities. Initially, a stochastic finite-time (SFT) H∞ state feedback controller and an SFT H∞ observer-based state feedback controller are constructed to realize the closed-loop control of systems. Then, based on the Lyapunov-Krasovskii functional (LKF) method, some sufficient conditions are established to guarantee that closed-loop systems (CLSs) satisfy SFT boundedness and SFT H∞ boundedness. Furthermore, the controller gains are obtained with the use of the linear matrix inequality (LMI) approach. In the end, numerical examples reveal the reasonableness and effectiveness of the proposed designing schemes.

Guaranteed cost event-triggered H∞ control of uncertain linear system via output disturbance observer

This paper is concerned with anti-disturbance output feedback control of uncertain systems via dynamic guaranteed cost triggering mechanism. An output disturbance observer is constructed to attenuate matched disturbances and the mismatched one is attenuated by the H∞ approach. A new dynamic event-triggered mechanism is established in terms of guaranteed cost triggering condition and triggering threshold. A composite controller is built on an observer based state feedback controller and an output disturbance compensator. By employing the Lyapunov stability method, a sufficient condition is presented in the framework of linear matrix inequality to ensure the asymptotic stability of the closed-loop system with the prescribed cost. Comparative simulation studies are supplied to verify the effectiveness of the proposed composite control scheme.

Visual Observer-Based State-Feedback Autonomous Motion Control on SE(3)

This paper introduces a visual observer-based state-feedback control tailored for autonomous motion on SE(3) to address challenges posed by modeling uncertainties and measurement noise. The proposed approach unfolds in two fundamental phases. In the initial stage, the visual observer, based on modeling information, visual sensors, and pre-deployed landmarks, along with the state-feedback controller, are developed independently, underpinning their individual semi-global practical asymptotic (SPA) stability. This modular approach ensures a robust foundation for the subsequent synthesis. The latter stage applies the well-established Small Gain Principle to regulate observer and controller parameters to guarantee the SPA stability of the closed-loop system with the visual-observer based state feedback control. The effectiveness of the proposed method is validated through simulation and experiments.

Design and implementation of trajectory planning for a high-order bounded reference

In control engineering, control processes are regulated to prevent transient shocks to test rigs. As an important part of the control loop, the reference may be continuous and bounded to avoid the transient impulse generated by the controller. Therefore, a high-order bounded reference (HOBR) is proposed for the trajectory generation. This paper studies the smooth control process and constrained reference generation for large testing platforms. Utilizing the Hermite interpolation technique, a planning method for the HOBR is proposed to ensure a smooth and bounder generated trajectory, which derives an analytic function for the desired reference. In addition, an observer-based state feedback controller is presented and applied to enable the system output to converge asymptotically to the desired reference. The theoretical analysis shows that the HOBR satisfies continuous constraints and boundary constraints at the same time. Finally, the effectiveness of the proposed HOBR in two constraints is demonstrated by both simulations and experiments.

Linear Matrix Inequality Design of Exponentially Stabilizing Observer-Based State Feedback Port-Hamiltonian Controllers

The design of an observer-based state feedback (OBSF) controller with guaranteed passivity properties for port-Hamiltonian systems (PHS) is addressed using linear matrix inequalities (LMIs). The observer gain is freely chosen and the LMIs conditions such that the state feedback is equivalent to control by interconnection with an input strictly passive (ISP) and/or an output strictly passive (OSP) and zero state detectable (ZSD) port-Hamiltonian controller are established. It is shown that the proposed controller exponentially stabilizes a class of infinite-dimensional PHS and asymptotically stabilizes a class of finite-dimensional non-linear PHS. A Timoshenko beam model and a microelectromechanical system are used to illustrate the proposed approach.

Observer-Based Control of a Microrobot Navigating within a 3D Blood Vessel along a Trajectory Delivered by a Joystick Device

In this paper, an observer-based state feedback control strategy for trajectory tracking of a magnetic microrobot navigating within a 3D blood vessel is proposed. The desired trajectory to be followed by the microrobot is generated by an operator using a joystick device. To deal with the significant effect of both external disturbances and parametric uncertainties, often encountered in biological environments, a state feedback stabilization, that enforces the output tracking despite any environmental disturbances, is developed. Then, for the purpose of implementation, a state observer is developed to recover the whole state from the measured position of the microrobot. The state feedback and observer gains are determined separately by solving a set of linear matrix inequalities derived in the framework of Lyapunov stability theory. Simulation runs are performed to demonstrate the performance of the proposed control strategy.

Impulsive observer-based admissibilization for delayed degenerate jump systems and application to DCM-IP device

This paper researches the impulsive observer-based admissibilization for delayed degenerate Markovian jump systems with completely known or partly unknown transition rates. In contrast with the normal continuous-time observer, the advantage of the impulsive observer is that it uses only the measurement outputs at the impulses moments to estimate the states of the controlled system. In order to make the obtained results more universalist, a novel piecewise differentiable Lyapunov–Krasovskii functional with piecewise linear impulse auxiliary functions is established, which can grasp the mixed characteristics of impulses instants information and Markovian jumping modes information. At the same time, singular value decomposition (SVD) technology is used to surmount the influence of the internal impulses of the degenerate system. Improved sufficient conditions about stochastic admissibilization for delayed degenerate impulsive Markovian jump systems are obtained in the form of linear matrix inequalities (LMIs) via mode-dependent impulsive observer-based state feedback controller. Direct current motor-controlled inverted pendulum (DCM-IP) device and a numerical example are utilized to verify the validity and practicability of the results acquired in this paper.

Self-triggered resilient stabilization of linear systems with quantized outputs

This paper studies the problem of stabilizing a self-triggered control system with quantized output. Employing a standard observer-based state feedback control law, a self-triggering mechanism that dictates the next sampling time based on quantized output is co-developed with an output encoding scheme. If, in addition, the transmission protocols at the controller-to-actuator (C–A) and sensor-to-controller (S–C) channels can be adapted, the self-triggered control architecture can be considerably simplified, leveraging a delicate observer-based deadbeat controller to eliminate the need for running the controller in parallel at the encoder side. To account for denial-of-service (DoS) in the S–C channel, the proposed output encoding and self-triggered control schemes are further made resilient. It is shown that a linear time-invariant system can be exponentially stabilized if some conditions on the average DoS duration time are met. There is a trade-off between the maximum inter-sampling time and the resilience against DoS attacks. Finally, a numerical example is presented to demonstrate the practical merits of the proposed self-triggered control schemes and associated theory.

Adaptive Finite-Time Control for a Class of p-Normal Nonlinear Systems

Compared with asymptotic stability or exponential stability, finite-time stability has the advantages of fast convergence, high tracking accuracy, and strong robustness. Therefore, finite-time control problem has received extensive attention. An adaptive finite-time control problem is discussed in this brief for a class of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> -normal nonlinear systems. First, an observer-based state feedback controller is constructed such that the nominal system is globally finite-time stable. Then, the nonlinear terms are dominated by introducing a dynamic gain. Based on Lyapunov stability theory, it is proved that the system state converges to origin in a finite time and the dynamic gain is bounded. Finally, an example is used to illustrate the effectiveness of the proposed control strategy.

Nonlinear Impulsive Control Design for Biologically Grounded NSM Tumor Growth Model Using Exact Linearized Mapping

This paper investigates the problem of personalized chemotherapy scheduling using a system-modeling approach based on a nonlinear impulsive control technique. In particular, this work deals with the so-called Norton-Simon-Massagué (NSM) model, a minimal biologically grounded model for controlled tumor growth, which has been accepted in clinical oncology for breast cancer treatment. In this paper, we continue this line of research, to advance the concept of closed-loop control a step further towards widespread clinical use. In the present work, the problem of chemotherapy drug scheduling is approached using an impulsive control strategy combined with a state-space observer. The technical challenges of the nonlinearity of the controlled system and the impulsive nature of control input are handled via the utilization of a novel mapping that transforms the control problem into a “simplified” linear discrete-time control problem. Theoretical guarantees regarding the sign and invertibility of the proposed transformation are demonstrated. Then, an observer-based state feedback controller is proposed for chemotherapy drug scheduling as a proof-of-concept control strategy. Simulation results showing the performance of the designed closed-loop controlled chemotherapy schedules in reducing and eradicating tumor volume are provided using model's parameters derived using real tumor data and Doxirubicin drug.

A Digital Observer-Based Repetitive Learning Composite Control Method for Large Range Piezo-Driven Nanopositioning Systems

In this study, a novel digital compound compensation method is proposed to compensate for the hysteresis nonlinearity and the drift disturbance of a piezoelectric nanopositioning system with a large range. The overall hysteresis behaviors can be divided into the static amplitude-dependent behavior and the dynamic rate-dependent behavior, where the static hysteresis is compensated for by a novel discrete feedforward controller, while the dynamic hysteresis and the drift disturbance are compensated for by a novel discrete composite feedback controller composed of a drift observer-based state feedback controller and a repetitive learning controller. Compared with traditional control strategies, the proposed compound control strategy, including feedforward and feedback components, can eliminate system errors more effectively when tracking large range signals with obvious hysteresis. Moreover, the proposed online drift observer is superior over a traditional offline drift compensator both in response speed and compensation accuracy. Sufficient simulation tests and convincing tracking experiments, with large range periodic signals up to 90 μm, are carried out. And comparisons with the two classical control algorithms are performed. The tracking results show that the mean absolute error of the proposed control method is minor compared with the other two algorithms, which validates that the proposed strategy can efficiently compensate for the hysteresis nonlinearity and the drift disturbance.

A data‐driven fault detection and fault‐tolerant control scheme for large‐scale systems and its application on multi‐area interconnected power systems

Stimulated by the enhancing requirements for system safety as well as process reliability in complex industrial processes, this paper investigates a data-driven fault detection and fault-tolerant control scheme for large-scale systems. To this end, a pair-wise decomposition approach is first presented based on the inclusion principle, which expands the original large-scale system into a set of disjointed pair-wise subsystems. Then, for the pair-wise subsystems, the observer-based residual generators and observer-based state feedback controllers for fault detection and fault-tolerant control purpose are further developed in a decentralized way. On this basis, the fault-tolerant controller for the original large-scale system is obtained by the coordination and contraction of the decentralized observer-based state feedback controllers. Finally, the feasibility and effectiveness of the proposed scheme are demonstrated through the case study on a multi-area interconnected power system.

Control for plasma glucose regulation in type 1 diabetes mellitus patients with unknown input delays

This paper presents a control strategy for plasma glucose regulation in the presence of input with unknown time delay (constant or variable) and meal disturbances in the system. The control scheme proposed is an observer-based state feedback controller. The observer achieves to estimate the state vector even if the control input in the system presents an unknown time delay in the input. The main advantage of the controller is that the gains are selected so the control law will provide positive values that ensure an implementable case. The observer-based control scheme is validated considering different disturbance and unknown delays scenarios, in both cases, glucose regulation is achieved, rejecting meal disturbances in 4 hours and avoiding hypoglycemic episodes.

Event-Triggered Control of Robotic Fish With Reduced Communication Rate

Underwater robots often need to communicate with external localization sensors. The low bandwidth in such communications is one of the bottlenecks in achieving accurate tracking control. Toward this end, we adopt a novel periodic event-triggered control (PETC) which allows a robotic fish to reduce its communication load in tracking a desired heading angle with position feedback from an external sensor. To design the PETC, a linear state-space model is derived from a nonlinear dynamic model of the robotic fish with a small perturbation assumption. The PETC consists of an observer, state-feedback controller, integrator, event-trigger rule, and predictor. The observer and state-feedback controller are designed to drive the tracking error to zero. The integrator reduces the steady-state error. The event-trigger rule determines when communication is needed while ensuring the efficacy of the state-feedback controller, and the predictor predicts the state vector for the state-feedback controller when communication is not available. For comparison, an observer-based state feedback control (OSFC) and a proportional-integral-derivative (PID) control are implemented in real-time experiments. Simulations and experimental results show that the PETC can dramatically reduce the number of communication instances without significantly degrading tracking performance, thereby saving communication energy and reducing the need for high bandwidth underwater communication.

Event-triggered control with waiting time based on state observer for switched linear systems

This paper concentrates on the state observer–based event-triggered control problem for a class of switched linear systems with external disturbance and transmission delay. It is assumed that the controller can only access the transmitted information of the state observer at each delayed event-triggered instant with a waiting time. First, by adopting the multiple Lyapunov–Krasovskii functional method, some sufficient conditions are derived for the establishment of the state observer, the input-to-state stability (ISS) and the globally uniformly exponential stability (GUES) of the switched linear systems under adjacent mode-dependent average dwell time (AMDADT) scheme. Then, we propose a state observer-based event-triggered sampling mechanism with waiting time and design an observer-based state feedback controller for the considered switched systems. Under the proposed event-triggered mechanism, the Zeno behavior can be easily excluded in all sampling processes. Finally, a numerical example is included to validate the proposed theory.

Finite-dimensional output stabilization for a class of linear distributed parameter systems — A small-gain approach

A small-gain approach is proposed to analyze closed-loop stability of linear diffusion-reaction systems under finite-dimensional observer-based state feedback control. For this, the decomposition of the infinite-dimensional system into a finite-dimensional slow subsystem used for design and an infinite-dimensional residual fast subsystem is considered. The effect of observer spillover in terms of a particular (dynamic) interconnection of the subsystems is thoroughly analyzed for in-domain and boundary control as well as sensing. This leads to the application of a small-gain theorem for interconnected systems based on input-to-output stability and unbounded observability properties. Moreover, an approach is presented for the computation of the required dimension of the slow subsystem used for controller design. Simulation scenarios for both scalar and coupled linear diffusion-reaction systems are used to underline the theoretical assessment and to give insight into the resulting properties of the interconnected systems.

Robust Feedback Control for Discrete-Time Systems Based on Iterative LMIs with Polytopic Uncertainty Representations Subject to Stochastic Noise

This paper deals with the design of linear observer-based state feedback controllers with constant gains for a class of nonlinear discrete-time systems in the form of a quasi-linear representation in presence of stochastic noise. For taking into account nonlinearities in the design of linear observer-based state feedback controllers, a polytopic modeling approach is investigated. An optimization problem is formulated to reduce the sensitivity of the controlled system towards stochastic input, state, and output noise with a predefined covariance. Due to the nonlinearities, the separation principle does not hold, thus, the controller and the observer have to be designed simultaneously. For this purpose, a Lyapunov-based method is used, which provides, in addition to the controller and observer gains, a stability proof for the nonlinear closed loop in a predefined polytopic domain. In general, this leads to nonlinear matrix inequalities. To solve these nonlinear matrix inequalities efficiently, we propose an approach based on linear matrix inequalities (LMIs) with a superposed iteration rule. When using this iterative LMI approach, a minimization task can be solved additionally, which desensitizes the closed loop to stochastic noise. The proposed method additionally enables the consideration of different linear closed loop structures by a unified Lyapunov-based framework. The efficiency of the proposed approach is demonstrated and compared with a classical LQG approach for a nonlinear overhead traveling crane.

State-Space PID: A Missing Link Between Classical and Modern Control

PID control is widely applied in industry. However, it is classified as a classical control technique, in that transfer function method is used to represent the ideal and/or practical PID controller. Modern control concepts, such as state feedback, observer, are seldom found in PID research. This paper proposes a state-space PID structure to fill the gap. The classical ideal PID is first shown to be a state-feedback control structure with the plant output and its derivative and integral as the states, and then a model-independent observer is proposed to estimate the states, thus approximate the ideal PID as a observer-based state feedback control structure (state-space PID). Then it is shown that the proposed state-space PID structure is the dual of the linear active disturbance rejection control structure, and it is a general-purposed control structure in that any strictly-proper linear controller with integration can be implemented via the proposed structure. The design of the state-space PID can be done via the well-known pole placement algorithm in modern control. Simulation and experiment results show that state-space PID structure is a practical implementation of ideal PID, which naturally integrates the noise reduction that is separated from PID tuning, and it is a natural generalization of the classical PID to high-order cases.