Abstract
In this paper, B-transform is applied to some impulsive control models and closed solution forms for the models obtained. The problems solved via the B-transform are the third order linear impulsive control systems with bang-bang control, Impulsive delay control systems, Impulsive heat control systems, the Impulsive diffusion problem and the impulsive Gross berg control model. Simulation for the bang bang model show that the solutions are negative and positive in some for given time interval. The solutions also exhibit non-periodic and non-oscillatory behaviour in the given interval. The solutions of impulsive diffusion model possess singularities in given interval of simulation.
Highlights
Impulses are small perturbations acting on a system for short moment of times and can take the form of “jumps”, rapid changes in the system or “shocks”, short-time mechanical impacts on two or more moving systems etc ([3, 12]).Many impulsive physical and biological processes occur in nature; the thermionic current in a vacuum tube is not smooth flow of electrons but is subject to fluctuation due to the random emission of electron from the cathode
Impulsive control systems (ICS) are control systems characterized by short time jumps and shocks that act on the system rapidly
It is worthy to note that the B-transform was developed by Oyelami and Ale (See [7, 9, 14]) for finding closed solution forms to the fixed moment impulsive systems
Summary
Impulses are small perturbations acting on a system for short moment of times and can take the form of “jumps”, rapid changes in the system or “shocks”, short-time mechanical impacts on two or more moving systems etc ([3, 12]). Many impulsive physical and biological processes occur in nature; the thermionic current in a vacuum tube is not smooth flow of electrons but is subject to fluctuation due to the random emission of electron from the cathode This phenomenon is called the small-short effect and was discovered by Schotty [7]. It is worthy to note that the B-transform was developed by Oyelami and Ale (See [7, 9, 14]) for finding closed solution forms to the fixed moment impulsive systems. In the recent times several models are evolving in attempt to some challenging problems in science and technology Some of these problem are from the control systems that of impulsive family. It is recommended that more concerted efforts be devoted to the theory
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