Observer design
Pro Research Analysisby 
Searched over 200M research papers for "observer design"
Observer Design: A Comprehensive Overview
Introduction to Observer Design
Observer design is a critical aspect of control theory, focusing on estimating the internal states of a system from its outputs. This is essential for systems where not all states are directly measurable. Various methodologies have been developed to address observer design for different types of systems, including linear, nonlinear, time-delay, and systems with unknown inputs.
Observer Design for Non-Smooth and Discontinuous Systems
Piece-Wise Linear Observers
For non-smooth and discontinuous systems, piece-wise linear observers have been effectively implemented. These observers are particularly useful for systems with one-sided restoring characteristics, such as a harmonically excited flexible steel beam with a one-sided support. They ensure global asymptotic stability of the estimation error dynamics, both in theory and practice1.
Dynamic Rotor Systems
In dynamic rotor systems, which serve as benchmarks for motion systems with friction and flexibility, observers have been developed to guarantee global asymptotic stability. These systems benefit from switched observers that achieve state reconstruction despite the non-smooth and discontinuous nature of the system1.
Nonlinear Observer Design
Observer Error Linearization
The observer error linearization approach is a robust method for designing observers for nonlinear systems. This method provides necessary and sufficient conditions for the existence of a linearization transformation, which simplifies the observer design process. This approach is applicable to both systems with and without inputs, offering a comprehensive solution for nonlinear observer design2.
Riccati Equation-Based Observers
For a class of nonlinear systems characterized by globally Lipschitz nonlinearities, observers can be designed using an off-line solution of a Riccati equation. This method is versatile, providing globally valid results for certain systems and approximate observers for more general nonlinear systems. An example application includes a single-link flexible joint robot, where the observer estimates the robot link variables based on joint measurements4.
Linear Time-Delay Systems
Generalized Coordinate Change
In linear systems with time delays, observer design can be achieved by finding a generalized coordinate change. This transformation ensures that all time-delay terms are injected by the system's output, which is guaranteed by a rank condition on the observability matrix. This method is particularly novel in multiple-output cases, where dimensional expansion in the coordinate change may be necessary3.
Hybrid Systems Approach
Aperiodic Sampled-Data Systems
For linear systems with aperiodic sampled-data measurements, a hybrid observer design is proposed. This observer uses two output injection terms: one at the sampling instants and another providing intersample injection. The error dynamics are analyzed using hybrid system tools, and Lyapunov theory is employed to ensure convergence. This approach is optimized using LMI-based design for observer gains5.
Piecewise Linear Systems
Luenberger-Type Observers
For bi-modal piecewise linear systems, both continuous and discrete time, Luenberger-type observers are effective. These observers ensure that the observation error dynamics are globally asymptotically stable when the system dynamics are continuous over the switching plane. For discontinuous dynamics, conditions are derived to ensure that the relative estimation error remains asymptotically small6.
Data-Driven Observer Design
Neural Canonical Observer Structures
An indirect data-driven approach using neural canonical observer structures is proposed for nonlinear discrete-time systems. This method employs an artificial neural network auto-encoder trained with recorded state, input, and output data. The neural approximations are used to construct an observer with linear error dynamics, demonstrated on both academic and industrial examples7.
Systems with Unknown Inputs
Projection-Based and Sliding Mode Observers
For systems with unknown inputs, two observer design approaches are proposed. The first approach decomposes the state into known and unknown components, using a dynamical system to estimate the unknown component. The second approach combines sliding modes and Lyapunov's second method to create a nonlinear observer that forces the observation error into a sliding mode along a manifold in the observation error space8.
Decentralized Design for Distributed Systems
Completely Decentralized Observers
A decentralized design for distributed state observers in continuous-time linear time-invariant plants is presented. Each agent in the system compensates for the lack of detectability through local communication with neighboring agents. This design allows for plug-and-play operation, enabling new agents to join or leave the network without disrupting the overall system9.
Conclusion
Observer design is a multifaceted field with various approaches tailored to different system characteristics. From non-smooth and discontinuous systems to nonlinear, time-delay, and systems with unknown inputs, each methodology offers unique advantages. The continuous development in this field ensures robust and efficient state estimation, crucial for advanced control systems.
Sources and full results
Most relevant research papers on this topic
Observer Designs for Experimental Non-Smooth and Discontinuous Systems
Observer designs for non-smooth mechanical systems can effectively reconstruct state reconstruction, ensuring global asymptotic stability in estimation error dynamics.
Nonlinear observer design by observer error linearization
This paper presents a computation procedure and necessary and sufficient conditions for observer design in nonlinear systems with and without inputs, proving the observer error linearization approach effective for both systems.
Highly CitedAn observer design for linear time-delay systems
This observer design for linear time-delay systems allows for a generalized coordinate change, ensuring that all time-delay terms are injected by the system's output, and allows for multiple-output cases.
Highly CitedObserver design for a class of nonlinear systems
The proposed methodology effectively constructs observers for nonlinear systems, yielding approximate results locally, and is applied to a single-link flexible joint robot.
Highly CitedObserver Design for Linear Aperiodic Sampled-Data Systems: A Hybrid Systems Approach
The hybrid observer design effectively optimizes observer gains in linear aperiodic sampled-data systems, with two output injection terms and a timer variable triggering new measurements.
Observer design for a class of piecewise linear systems
This paper presents observer design procedures for bi-modal piecewise linear systems in both continuous and discrete time, ensuring globally asymptotically stable observation error dynamics and asymptotic small relative estimation error.
Indirect Data-Driven Observer Design Using Neural Canonical Observer Structures
This paper proposes an indirect data-driven observer design approach for nonlinear discrete-time systems using neural canonical observer structures, enabling linear error dynamics using linear control theory methods.
Observer design for systems with unknown inputs
This paper proposes two design procedures for observers for systems with unknown inputs, one using projection operators and the other combining sliding modes and Lyapunov's second method.
Highly CitedCompletely Decentralized Design of Distributed Observer for Linear Systems
This paper presents a decentralized design of a distributed state observer for linear systems, enabling plug-and-play operation and enabling each agent to recover its own detectable information while compensating the undetectable portion through local communication with neighboring agents.
Observer design — A survey
Observer design for linear time-invariant open-loop systems can be simplified and optimized, with a new generalized state feedback control principle providing strong enough feedback for most applications.
Try another search
What are the latest treatments for migraine prevention?
What are the best practices for prenatal nutrition?
What are the causes and consequences of antibiotic resistance?
What are the basic components and functions of the nervous system?
What are the causes and consequences of neurodegenerative diseases?
real estate is a good inflation hedge