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State observation is a fundamental component of modern control theory. In discrete-time format, the standard observer is one-step ahead. It estimates of the system state at the next time step k + \ based on information available at the... more
State observation is a fundamental component of modern control theory. In discrete-time format, the standard observer is one-step ahead. It estimates of the system state at the next time step k + \ based on information available at the current time step k. For multi-step ahead prediction (to estimate the state at time step k + a, for some o t>l ) , one can repeatedly propagate the one-step estimation a times into the future, but this process tends to accumulate errors from one propagation to the next. This paper introduces the notion of an observer which directly predicts the state of the system at a some specified time step in the future based on current information. More importantly, this multiple-step ahead observer, which involves the system controllability matrix, is identified directly from input-output data. Hence, there is no need for a model of the system before hand. One possible application of a multi-step ahead observer is in receding-horizon predictive control, which bases its control action at the present time on a prediction of the system response at some time step in the future. If desired, it is possible to recover the usual one-step ahead state-space model of the system from the identified multiple-step ahead observer as well, although a stabilizing feedback controller can be designed from the identified observer directly. Numerical examples will be used to illustrate the key identification and control aspects of this formulation.
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In state-space system identification theory, the Hankel matrix often appears prior to model realization. Traditionally, one identifies from input-output data the Markov parameters from which the Hankel matrix is built. This paper examines... more
In state-space system identification theory, the Hankel matrix often appears prior to model realization. Traditionally, one identifies from input-output data the Markov parameters from which the Hankel matrix is built. This paper examines the strategy where the Hankel matrix itself is identified from input-output data. Various options are examined along this direction where the identification of the Hankel matrix can
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The ARMarkov models were originally developed for adaptive neural control, and later for predictive control, and state-space identification. Recently, an interaction matrix formulation has been developed that explains the internal... more
The ARMarkov models were originally developed for adaptive neural control, and later for predictive control, and state-space identification. Recently, an interaction matrix formulation has been developed that explains the internal structure of the ARMarkov models and their connection to the state-space representation. Using the interaction matrix formulation, we show in this paper how a state estimator can be identified directly
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Predictive control refers to the concept where the current control decision is based on a prediction of the system controlled response a number of times into the future. Originally derived from input-output models, recent years have seen... more
Predictive control refers to the concept where the current control decision is based on a prediction of the system controlled response a number of times into the future. Originally derived from input-output models, recent years have seen efforts to interpret and develop predictive control from the state-space domain. This paper presents a formulation that unifies the two perspectives. Although a
Research Interests:
State observation is a fundamental component of modern control theory. In discrete-time format, the standard observer is one-step ahead. It estimates of the system state at the next time step k + \ based on information available at the... more
State observation is a fundamental component of modern control theory. In discrete-time format, the standard observer is one-step ahead. It estimates of the system state at the next time step k + \ based on information available at the current time step k. For multi-step ahead prediction (to estimate the state at time step k + a, for some o t>l ) , one can repeatedly propagate the one-step estimation a times into the future, but this process tends to accumulate errors from one propagation to the next. This paper introduces the notion of an observer which directly predicts the state of the system at a some specified time step in the future based on current information. More importantly, this multiple-step ahead observer, which involves the system controllability matrix, is identified directly from input-output data. Hence, there is no need for a model of the system before hand. One possible application of a multi-step ahead observer is in receding-horizon predictive control, which bases its control action at the present time on a prediction of the system response at some time step in the future. If desired, it is possible to recover the usual one-step ahead state-space model of the system from the identified multiple-step ahead observer as well, although a stabilizing feedback controller can be designed from the identified observer directly. Numerical examples will be used to illustrate the key identification and control aspects of this formulation.