By Hong Wang BSc, MEng, PhD (auth.)
Over the prior many years, even if stochastic method regulate has been studied intensively in the box of keep an eye on engineering, all of the modelling and keep watch over ideas constructed thus far have targeting the functionality of 1 or output homes of the approach, akin to minimum-variance keep an eye on or mean-value keep an eye on. the final assumption utilized in the formula of modelling and regulate ideas is that the distribution of the random indications concerned is Gaussian. during this publication, a suite of recent ways for the keep an eye on of the output likelihood density functionality of stochastic dynamic structures (those subjected to any bounded random inputs), has been constructed. during this context, the aim of keep watch over approach layout turns into the choice of a keep watch over sign that makes the form of the procedure output's p.d.f. as shut as attainable to a given distribution. The publication includes fabric at the topics of:
• keep watch over of single-input single-output and multiple-input multiple-output stochastic systems.
• solid adaptive keep watch over of stochastic distributions.
• version reference adaptive control.
• keep watch over of nonlinear dynamic stochastic systems.
• tracking of bounded stochastic distributions.
• regulate set of rules design.
• Singular stochastic systems.
A new illustration of dynamic stochastic platforms is produced by utilizing B-spline services to explain the output p.d.f.
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Extra info for Bounded Dynamic Stochastic Systems: Modelling and Control
A change in one part of the input space minimally affects the model response for other inputs. The input axes are divided into intervals by a set of values called knots. Knots serve as "address locations" for the univariate B-spline functions. Thus a knot vector for each input axis contains the knot values which subdivide that axis into intervals. The knots can be placed in any manner desired by the designer. Hence, a priori information can be incorporated into the network H. 3 Model representation 18 at this stage in the design.
Pter 3 Control of MIMO Stochastic Systems 49 From this equation, it can be clearly seen that the control sequence is nonlinear with respect to the use ofthe output tracking error signal V(k). 15) can be neglected. 18) which is the optimal control sequence minimising J when 01 0, and is, of course, linear with respect to the output tracking error. 19) where Amin(E) represents the minimum eigenvalue of matrix E. 19), the closed loop stability should be analysed in order to ensure the uniform boundness ofthe state vector x(k) when Vg is uniformly bounded.
In contrast to the existing on-line identification algorithms, at each sample time a set of outputs of the system are only used here to construct corresponding probability density function in order to estimate unknown parameters of the dynamic part of the system. 13) is similar to the DARMA model used in adaptive control (), the resulting control sequence Uk takes a totally different form and is generally nonlinear with respect to the measured output used in the control algorithms. However, for linear dynamic systems where Vk are available, the control sequence will be linear with respect to Vk.
Bounded Dynamic Stochastic Systems: Modelling and Control by Hong Wang BSc, MEng, PhD (auth.)