Kok Tin Tan’s research while affiliated with University of Michigan and other places

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Publications (4)


Discrete‐time reference governors and the nonlinear control of systems with state and control constraints
  • Article

August 1995

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47 Reads

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398 Citations

International Journal of Robust and Nonlinear Control

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Ilya Kolmanovsky

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Kok Tin Tan

Discrete-time, linear control systems with specified pointwise-in-time constraints, such as those imposed by actuator saturation, are considered. The constraints are enforced by the addition of a nonlinear ‘reference governor’ that attenuates, when necessary, the input commands. Because the constraints are satisfied, the control system remains linear and undesirable response effects such as instability due to saturation are avoided. The nonlinear action of the reference governor is defined in terms of a finitely determined maximal output admissible set and can be implemented on-line for systems of moderately high order. The main result is global in nature: if the input command converges to a statically admissible input and the initial state of the system belongs to the maximal output admissible set, the eventual action of the reference governor is a unit delay.


Nonlinear control of discrete-time linear systems with State and control constraints: a reference governor with global convergence properties

January 1995

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28 Reads

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129 Citations

Discrete-time, linear control systems with specified pointwise-in-time constraints, such as those imposed by actuator saturation, are considered. The constraints are enforced by the addition of a nonlinear “reference governor” that attenuates, when necessary, the input commands. Because the constraints are enforced, the control system remains linear and undesirable response effects such as instability due to saturation are avoided. The structure of the governor is a modification of the continuous-time reference governor proposed by Kapasouris, Athans and Stein (1990). Its nonlinear action is defined using an appropriate, finitely determined, maximal output admissible set. As a result, the governor can be implemented on-line for systems of significant order. Algorithmic details of the implementation are described. Theorems provide comprehensive results concerning the response of the overall system which are much stronger than those given in the above paper. The main result is global in nature: if the input command converges to a statically admissible input and the initial state of the system belongs to the maximal output admissible set, the eventual action of the reference governor is a unit delay. A tenth-order, helicopter system is considered as an example


Linear Systems with Output Constraints: The Theory and Application of Maximal Output Admissible Sets

July 1991

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107 Reads

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1,264 Citations

IEEE Transactions on Automatic Control

An initial state of an unforced linear system is output admissible with respect to a constraint set Y if the resulting output function satisfies the pointwise-in-time condition Y(t) ¿ Y,t ± 0. The set of all such initial states is the maximal output admissible set, O ¿ . The properties of O ¿ and its characterization are investigated. In the discrete-time case it is generally possible to represent O ¿ , or a close approximation of it, by a finite number of functional inequalities. Practical algorithms for generating the functions are described. O ¿ has important applications in the analysis and design of closed loop systems with state and control constraints. An example is given. The discrete-time results are used to obtain an alternative implementation of the error governor control scheme proposed by Kapasouris, Athans and Stein [6]. It works as well as their implementation, but reduces the computational load on the controller. by several orders of magnitude.


Citations (3)


... To address the limitations of MPC and barrier function methods, the Reference Governor (RG) [6] strategy was pro-posed. As its name suggests, the RG enforces the constraints by modifying the reference command of a pre-stabilized closed-loop system. ...

Reference:

A Machine Learning-Based Reference Governor for Nonlinear Systems With Application to Automotive Fuel Cells
Discrete‐time reference governors and the nonlinear control of systems with state and control constraints
  • Citing Article
  • August 1995

International Journal of Robust and Nonlinear Control

... The characterization of MOS has many useful applications in the design and analysis of closed-loop systems with state and control constraints [1][2][3]. This framework is essential for ensuring that system states remain within predefined bounds, which is crucial for the stability and performance of these systems. ...

Linear Systems with Output Constraints: The Theory and Application of Maximal Output Admissible Sets
  • Citing Conference Paper
  • July 1991

IEEE Transactions on Automatic Control

... More recently, this definition was extended from considering only outputs to considering every arbitrary combination of states and constant input signals. 8,9 The MOAS is very important for the design of many constrained control schemes. In particular, it is the key ingredient for the formulation of Reference/Command Governor schemes, 9 of multimode control schemes, 10 and is also a commonly used terminal set in Model Predictive Control (MPC) schemes. ...

Nonlinear control of discrete-time linear systems with State and control constraints: a reference governor with global convergence properties
  • Citing Conference Paper
  • January 1995