Adaptive stabilization of a discrete linear system with an unknown high-frequency gain

Mudgett, D.R.; Morse, A. Stephen

doi:10.1109/tac.1985.1104058

Cited by 21 publications

(15 citation statements)

References 6 publications

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“…For systems of the form (5.1) only two iterations are necessary to find out the correct sign S e {1, -1} of the control law u,: Sk,y,. In this sense the algorithm is much simpler than the one presented in Mudgett and Morse (1985). Proposition 6.…”

Section: Qi3)mentioning

confidence: 98%

“…Tnts pe.per addresses the problem of adaptively stabilizing first-order, single-input single-output, linear systems of the form to 0 < lbcl < g. To produce an asymptotically decaying output, the controller of Section 2 needs only a small modification and is much simpler than the one introduced by Mudgett and Morse (1985). These results are illustrated by some numerical simulations.…”

Section: Introductionmentioning

confidence: 99%

“…However, only a few authors tackled analogous questions and problems for discrete-time linear systems. Mudgett and Morse (1985) considered the class of time-invariant systems of the form (1.1) where only knowledge of an upper bound of lbcl is required. It is not obvious how their controller can be simplified if the sign of öc is known.…”

mentioning

confidence: 99%

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Robust adaptive stabilization of discrete-time first-order systems

Ilchmann

1991

Automatica

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Section: Qi3)mentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Robust adaptive stabilization of discrete-time first-order systems

Ilchmann

1991

Automatica

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“…Then, from the BOBI property in Assumption 6, the boundedness of is guaranteed. Using HONN as an approximator of , then the output feedback adaptive NN control is given as (28) Adding and subtracting on the right-hand side of (25) leads to (29) where with , according to the mean value theorem. For convenience, let us introduce the following notations: (30) and it is obvious that .…”

Section: Adaptive Nn Control Designmentioning

confidence: 99%

“…In discrete time, to solve the unknown control direction problem, a two-step adaptation law was proposed for a first-order discrete system without knowledge of control gain [28]. However, this procedure is limited to the first-order linear system.…”

mentioning

confidence: 99%

Output Feedback NN Control for Two Classes of Discrete-Time Systems With Unknown Control Directions in a Unified Approach

Yang

Chen

et al. 2008

IEEE Trans. Neural Netw.

206

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Abstract-In this paper, output feedback adaptive neural network (NN) controls are investigated for two classes of nonlinear discrete-time systems with unknown control directions: 1) nonlinear pure-feedback systems and 2) nonlinear autoregressive moving average with exogenous inputs (NARMAX) systems. To overcome the noncausal problem, which has been known to be a major obstacle in the discrete-time control design, both systems are transformed to a predictor for output feedback control design. Implicit function theorem is used to overcome the difficulty of the nonaffine appearance of the control input. The problem of lacking a priori knowledge on the control directions is solved by using discrete Nussbaum gain. The high-order neural network (HONN) is employed to approximate the unknown control. The closed-loop system achieves semiglobal uniformly-ultimately-bounded (SGUUB) stability and the output tracking error is made within a neighborhood around zero. Simulation results are presented to demonstrate the effectiveness of the proposed control.Index Terms-Discrete Nussbaum gain, discrete-time system, nonlinear autoregressive moving average with exogenous inputs (NARMAX) systems, neural networks (NNs), pure-feedback system, unknown control directions.

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Adaptive iterative learning control of discrete‐time varying systems with unknown control direction

Yan

Sun

2012

Adaptive Control & Signal

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Without using Nussbaum gain, a novel method is presented to solve the unknown control direction problem for discrete-time systems. The underlying idea is to fully exploit the convergence property of parameter estimates in well-known adaptive algorithms. By incorporating two modifications into the control and the parameter update laws, respectively, we present an adaptive iterative learning control scheme for discretetime varying systems without the prior knowledge of the sign of control gain. It is shown that the proposed adaptive iterative learning control can achieve perfect tracking over the finite time interval while all the closed-loop signals remain bounded. An illustrative example is presented to verify effectiveness of the proposed scheme.where p k is randomly iteration-variant in the interval OE0, 1.Define the performance index J k D max 16t 6200 jy k .t / y k .t /j. The iteration stops when J k < 0.01. The proposed adaptive ILC scheme is applied in the simulation. The tracking performance is achieved at the 57th iteration. Figure 2 shows the convergence history of the performance index J k . Figure 3 shows the system output y k .t / and the reference trajectory y k .t / at k D 57, which clearly shows that y k .t / converges to y k .t / for all t 2 f1, 2,, 200g. Figure 4 shows the control input u k .t / at k D 57. The singularity of the control law is successfully avoided via the proposed approach.

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Adaptive stabilization of a discrete linear system with an unknown high-frequency gain

Cited by 21 publications

References 6 publications

Robust adaptive stabilization of discrete-time first-order systems

Robust adaptive stabilization of discrete-time first-order systems

Output Feedback NN Control for Two Classes of Discrete-Time Systems With Unknown Control Directions in a Unified Approach

Adaptive iterative learning control of discrete‐time varying systems with unknown control direction

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