State Observer For Systems Research Articles

State Observation for Lipschitz Nonlinear Dynamical Systems Based on Lyapunov Functions and Functionals

State observers for systems having Lipschitz nonlinearities are considered for what concerns the stability of the estimation error by means of a decomposition of the dynamics of the error into the cascade of two systems. First, conditions are established in order to guarantee the asymptotic stability of the estimation error in a noise-free setting. Second, under the effect of system and measurement disturbances regarded as unknown inputs affecting the dynamics of the error, the proposed observers provide an estimation error that is input-to-state stable with respect to these disturbances. Lyapunov functions and functionals are adopted to prove such results. Third, simulations are shown to confirm the theoretical achievements and the effectiveness of the stability conditions we have established.

Multi-Agent Reinforcement Learning for Energy Harvesting Two-Hop Communications With a Partially Observable System State

We consider an energy harvesting (EH) transmitter communicating with a receiver through an EH relay. The harvested energy is used for data transmission, including the circuit energy consumption. As in practical scenarios, the system's state, comprised by the harvested energy, battery levels, data buffer levels, and channel gains, is only partially observable by the EH nodes. Moreover, the EH nodes have only outdated knowledge regarding the channel gains for their own transmit channels. Our goal is to find distributed transmission policies aiming at maximizing the throughput. A channel predictor based on a Kalman filter is implemented in each EH node to estimate the current channel gain for its own channel. Furthermore, to overcome the partial observability of the system's state, the EH nodes cooperate with each other to obtain information about their parameters during a signaling phase. We model the problem as a Markov game and propose a multi-agent reinforcement learning algorithm to find the transmission policies. We show the trade-off between the achievable throughput and the signaling required, and provide convergence guarantees for the proposed algorithm. Results show that even when the signaling overhead is taken into account, the proposed algorithm outperforms other approaches that do not consider cooperation.

Fault-tolerant control with state and disturbance observers for vehicle active suspension systems

This paper deals with the design of a fault-tolerant control scheme of active suspension systems for vehicle ride comfort. Unknown actuator failures from a variety of reasons cause performance deterioration of the active suspension controller. The proposed fault-tolerant control algorithm consists of two parts: a compensation for actuator failure and a fault mode selector. The main function of the fault compensation strategy is to estimate and compensate for the loss of effectiveness of the actuators. A suspension state observer and a disturbance observer operate simultaneously to determine the feedback control input. The controller and observer have been developed based on a reduced full-car dynamic model that contains only the vehicle body dynamics. The main advantage of the proposed observer is that an easily accessible and inexpensive measurement is only required and the effect of unknown road disturbance on the estimation error is completely removed. To cope with complete failure cases, the fault mode selector is also designed to redistribute the control input to the remaining healthy actuators. Tracking of the loss of effectiveness of the actuators is used for the fault model identification. The performance of the proposed approach has been evaluated via simulation studies. It is shown that the vehicle ride comfort in the presence of actuator faults can be improved by the proposed combined strategy of the fault compensation method and the fault mode selector.

Optimal PMUs placement considering ZIBs and single line and PMUs outages

Phasor measurement unit (PMU) is among the most important measurement devices in modern power systems. It measures the voltage and current phasors which have both magnitude and phase angle using a common timing reference. These measurements are utilized in real time applications of electrical power systems. The main drawback of PMUs is its high cost so if PMUs are used to collect or send online real data from a system to a data centre or a decision maker, the used number of PMUs should be minimum with full observability of system measurements. This paper proposes a flower pollination algorithm (FPA) to find the optimal number and locations of PMUs in power systems. The optimization objectives of the work are the minimization of PMUs number, the achievement of complete observability of power system states, and the maximization of measurement redundancy. Existence of zero-injection buses in the system decreases the number of PMUs that is required to fulfil the complete observability of system states. Furthermore, additional constraints for remaining system full observable following failure of single PMU and single line outage are also included to increase the system reliability. The performance and efficiency of the proposed FPA is tested on IEEE standard networks such as 14-bus, 30-bus, 57-bus and 118-bus and new England 39-bus network. The obtained simulation results approve the ability of the proposed optimization method to find the optimal allocation of PMUs in different cases with fulfilling complete observability and reliability of electric power systems. The superiority of FPA is also verified by comparing its results of other optimization algorithms.

DNN projectional observer for advanced ozonation systems of complex contaminants mixtures

The aim of this study is to provide a class of state observers, based on differential neural networks, to approximate a class of advanced oxidation systems, based on the application of ozone high oxidant power and catalyst (the named catalytic ozonation). The study considers the design of a state observer for uncertain systems with the restrictions of the ozonation system, including the positivity of the states, as well as the control action. The observer includes a projection operator which is motivated by the state constraints. The learning laws of the proposed differential neural networks are obtained using a class of controlled state restricted Lyapunov functions. The detailed stability analysis proves the input to state stability with respect to the modeling error, as well as the bounded uncertainties of the ozonation system. The experimental confirmation of the state estimation is also presented. The experimental case considers the ozonation of a toxic organic contaminant (therephtalic acid) which is a regular pollutant of the plastic industry wastewater.

Towards event-triggered extended state observer for multi-agent systems

This paper deals with the event-triggered leader-follower consensus problem of linear multi-agent systems with disturbances over the directed graph. By using relative output information of the neighboring agents, we develop a novel class of distributed extended state observers. With the estimated values of tracking error and coupled states of the leader’s input and disturbances, event-triggered protocols are designed to solve the leader-follower consensus problem. The proposed protocols update intermittently and can suppress disturbances actively. Subsequently, we prove the systems don’t exhibit Zeno behavior. Furthermore, both the input of leader and disturbances are considered as unmodeled and not available to any follower. Finally, a simulation example is provided to demonstrate the theoretical results.

Orbital stabilization of nonlinear systems via the immersion and invariance technique

SummaryImmersion and invariance is a technique for the design of stabilizing and adaptive controllers and state observers for nonlinear systems. In all these applications the problem considered is the stabilization of equilibrium points. Motivated by some modern applications, we show that the technique can also be used to solve the problem of orbital stabilization, where the final objective is to generate periodic solutions that are attractive. The feasibility of our result is illustrated by means of some classical mechanical engineering and power electronics examples.

Output Feedback Stabilization for an Axially Moving System

This paper presents a framework of output feedback stabilization of an axially moving accelerated system influenced by exogenous disturbances. Based on the flexible-rigid coupled dynamical model of the system, a boundary output feedback control is developed to reduce the vibration and estimate the boundary disturbance by fusing Lyapunov’s synthetic approach, disturbance rejection theory, and observer technique. Under the developed control, the exponential convergence of system state observer errors and uniformly ultimately bounded stability of the controlled system can be demonstrated adopting rigorous theoretical analysis, and the control performance of the developed control method is verified by simulation results.

State observers for reaction systems with improved convergence rates

The problem of designing state observers for reaction systems whose convergence rate is faster than the standard asymptotic observers [7] is addressed in this paper. It is assumed that the reaction functions are known and that there are more measurements than “independent” reactions. If the unmeasurable state enters linearly in the reaction functions we propose an observer that converges in finite-time, under very weak excitation assumptions. If this dependence is nonlinear, we additionally assume that there is an element of the reaction functions vector that depends only on one unmeasurable state and that these functions are strictly monotonic. Under these conditions, a state observer that ensures exponential convergence of the states that appear in the reaction functions is designed. For the unmeasurable states that do not appear in these functions, the convergence is similar to the one of the asymptotic observers.

Observer Design for Nonlinear Networked Control Systems With Persistently Exciting Protocols

We study the design of state observers for nonlinear networked control systems (NCSs) affected by disturbances and measurement noise, via an emulation-like approach. That is, given an observer designed with a specific stability property in the absence of communication constraints, we implement it over a network, and we provide sufficient conditions on the latter to preserve the stability property of the observer. In particular, we provide a bound on the maximum allowable transmission interval (MATI) that guarantees an input-to-state stability (ISS) property for the corresponding estimation error system. The stability analysis is trajectory-based, utilizes small-gain arguments, and exploits a persistently exciting property of the scheduling protocols. This property is key in our analysis and allows us to obtain significantly larger MATI bounds in comparison to the ones found in the literature. Our results hold for a general class of NCSs; however, we show that these results are also applicable to NCSs implemented over a specific physical network called WirelessHART (WH). The latter is mainly characterized by its multihop structure, slotted communication cycles, and the possibility to simultaneously transmit over different frequencies. We show that our results can be further improved by taking into account the intrinsic structure of the WH–NCS model. That is, we explicitly exploit the model structure in our analysis to obtain an even tighter MATI bound that guarantees the same ISS property for the estimation error system. Finally, to illustrate our results, we present analysis and numerical simulations for a class of Lipschitz nonlinear systems and high-gain observers.

A robust reduced-order observers design approach for linear discrete periodic systems

This paper investigates the problem of designing reduced-order observers for linear discrete-time periodic (LDP) systems. In case that the linear discrete-time periodic system is observable, an algebraic equivalent system is obtained by non-singular linear transformation, and the partial states to be observed are separated simultaneously. Then the considered problem is transformed into the problem of solving a class of periodic Sylvester matrix equation and an iterative algorithm for periodic reduced-order state observers design is derived. In addition, robust consideration based on periodic reduced-order state observers for LDP systems is also conducted. At last, one numerical example is worked out to illustrate the effectiveness of the proposed approaches.

Four-Wheel-Independent-Driving Electric Vehicles Stability Control Based on Yaw Rate and Side Slip Angle

In this paper, a nonlinear system state observer and a vehicle upper controller suitable for a four-wheel independent drive vehicle have been proposed. The observer uses Unscented Kalman Filter to observe the longitudinal speed, lateral velocity and yaw rate of the vehicle, and then calculates the side slip angle of the vehicle. The upper controller adopts the control method of yaw rate and side slip angle combined with Sliding Mode Control to calculate the target yaw moment. Finally, the CARSIM-MATLAB co-simulation is carried out to verify the proposed control strategy. The simulation results indicate that the proposed control strategy enables the vehicle to effectively track the target yaw rate and side slip angle simultaneously, ensuring vehicle stability and safety.

State estimators and observers for continuous and discrete linear systems. Part 2. Integral observers for exact state reconstruction

In the paper, the exact state observers will be presented. The state estimators and observers can be used in technical processes for many purposes like the fault detection and diagnosis, the implementation of the state controllers, and soft reconstruction of inaccessible for measurements variables of the system. As the standard, for continuous systems the differential estimators of Kalman filter or Luenberger type observer are commonly used. However, if the initial conditions of the real state are unknown, both estimators guarantee only an asymptotic quality of the real state tracking. The paper presents another type of the state observers, which for continuous system have the structure given by two integral operators. Based on measurements of the system input and output signals on some predefined finite time interval T, they can reconstruct the initial state exactly. In on-line version, the exact state reconstruction is performed continuously for every t, based on special procedure executed within two moving windows of width T, on sliding time interval [t-T, t].

Distributed fault‐tolerant model predictive control for intermittent faults

Intermittent fault is a special kind of fault form, which often occurs in industry processes but has been less studied. This study focuses on the distributed fault-tolerant model predictive control (DFTMPC) problem for an intermittent fault in actuators or sensors. A novel state observer and DFTMPC controller integral framework are presented. The proposed distributed system state observer can both deal with the unknown inputs and compensate for the interconnected variables' estimation errors, achieving a more accurate estimation. A fault mode-switched model is constructed to describe the system with multi-intermittent faults in a hidden way. This allows us to design a distributed fault-tolerant controller without reconfiguration. For the proposed distributed model predictive controller, asymptotically stable conditions are given, meanwhile, the whole algorithm for multi-intermittent fault-tolerant control is concluded. A numerical example is simulated to verify the proposed method.

A modeling error-based adaptive fuzzy observer approach with input saturation analysis for robust control of affine and non-affine systems

In this paper, a robust control approach is applied for both MIMO/SISO affine/non-affine nonlinear systems based on a modeling error-based adaptive fuzzy observer controller, in the presence of input saturation. In the proposed scheme, non-affine nonlinear systems can be transformed to affine systems and unknown higher-order term of expansion (HOTE) that appears due to the use of this method can be estimated by an adaptive fuzzy technique. Using the modeling error between the system states observer and a serial–parallel estimator model, a modeling error-based adaptive fuzzy observer estimator is proposed that uses the modeling error as the input of fuzzy system to approximate and adaptively compensate the unknown HOTE and also the external disturbance. The proposed scheme is able to hold control performance in the presence of input saturation. An analysis of the controlled system is presented to verify the stability of the system under control. The stability of the closed-loop system is provided based on the strictly positive real condition and Lyapunov theory. The proposed approach is effectual and robust. The simulation results demonstrate the usefulness of the proposed method for both MIMO and SISO systems.

Data-driven adaptive dynamic programming for partially observable nonzero-sum games via Q-learning method

ABSTRACTThis paper concerns with a class of discrete-time linear nonzero-sum games with the partially observable system state. As is known, the optimal control policy for the nonzero-sum games relies on the full state measurement which is hard to fulfil in partially observable environment. Moreover, to achieve the optimal control, one needs to know the accurate system model. To overcome these deficiencies, this paper develops a data-driven adaptive dynamic programming method via Q-learning method using measurable input/output data without any system knowledge. First, the representation of the unmeasurable inner system state is built using historical input/output data. Then, based on the representation state, a Q-function-based policy iteration approach with convergence analysis is introduced to approximate the optimal control policy iteratively. A neural network (NN)-based actor-critic framework is applied to implement the developed data-driven approach. Finally, two simulation examples are provided to demonstrate the effectiveness of the developed approach.

Event-triggered predictor-based control with gain-Scheduling and extended state observer for networked control systems

This paper investigates the stabilization of Networked Control Systems (NCS) with mismatched disturbances through a novel Event-Triggered Control (ETC), composed of a predictor-feedback scheme and a gain-scheduled Extended State Observer (ESO). The key idea of the proposed control strategy is threefold: (i) to reduce resource usage in the NCS (bandwidth, energy) while maintaining a satisfactory control performance; (ii) to counteract the main negative effects of NCS: time-varying delays, packet dropouts, packet disorder, and (iii) to reject the steady-state error in the controlled output due to mismatched disturbances. Moreover, we address the co-design of the controller/observer gains, together with the event-triggered parameters, by means of Linear Matrix Inequalities (LMI) and Cone Complementarity Linearization (CCL) approaches. Finally, we illustrate the effectiveness of the proposed control synthesis by simulation and experimental results in a Unmanned Aerial Vehicle (UAV) based test-bed platform.

On State Observers for Nonlinear Systems: A New Design and a Unifying Framework

In this paper we propose a new observer design technique for nonlinear systems. It combines the well-known Kazantzis-Kravaris-Luenberger observer and the recently introduced parameter estimation-based observer, which become special cases of it---extending the realm of applicability of both methods. A second contribution of the paper is the proof that these designs can be recast as particular cases of immersion and invariance observers---providing in this way a unified framework for their analysis and design. Simulation results of a physical system that illustrates the superior performance of the proposed observer compared to other existing observers are presented.

State Estimation for Linear Time-Varying Observation Systems

We consider the state observation and estimation problems for linear time-varying systems of ordinary differential equations. We show that the uniform observability is equivalent to the approximate observability, i.e., the possibility of using delta sequences to estimate the current state with arbitrary accuracy without differentiating the output function. We propose a method for constructing state estimators for linear time-varying systems based on the quasi-differentiability of the coefficients with respect to a specially constructed lower-triangular matrix. For uniformly observable systems with quasi-differentiable coefficients, we obtain conditions for the existence of an exponential observer and describe a constructive method for designing such observers.

Assessing seismic vulnerability of urban road networks by a Bayesian network approach

Evaluating the seismic vulnerability of urban road network is important for proactive reinforcement of the weakest link of the road network and post-disaster response and recovery of infrastructure systems. The paper proposes a Bayesian network (BN) method for seismic vulnerability assessment of an urban road network considering spatial seismic hazard with different levels of ground motion intensities, vulnerability of the components and effect of structural damage of components within the road network to the network functionality.Seismic vulnerability of the components in the road network is quantified based on physical structural damage under the earthquake demand. The vulnerability of the network is evaluated in terms of its dis-connectivity due to structural damage and induced transportation functional loss. BN model is built with vulnerability of the components as prior probability. The BN structure and CPT (Conditional Probability Table) is established based on transportation network analysis. The dis-connectivity of the road network is updated in light of information obtained from the observation of system or component states. Thus, the posterior probability could be calculated to identify the critical links and assess the seismic vulnerability of road network respectively. A case study is presented to show the application of the method. Results may contribute to the decision making on the reinforcement of the road network and the management of available resources to improve the disaster resilience and functionality of transportation systems in terms of seismic vulnerability.