Abstract: In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.
Abstract: In this paper, using (G/G )-expansion method and modified F-expansion method, we give some explicit formulas of exact traveling wave solutions for the (3+1)-dimensional breaking soliton equation. A modified F-expansion method is proposed by taking full advantages of F-expansion method and Riccati equation in seeking exact solutions of the equation.
Abstract: In this paper the optimal control strategy for
Permanent Magnet Synchronous Motor (PMSM) based drive system
is presented. The designed full optimal control is available for speed
operating range up to base speed. The optimal voltage space-vector
assures input energy reduction and stator loss minimization,
maintaining the output energy in the same limits with the
conventional PMSM electrical drive. The optimal control with three
components is based on the energetically criteria and it is applicable
in numerical version, being a nonrecursive solution. The simulation
results confirm the increased efficiency of the optimal PMSM drive.
The properties of the optimal voltage space vector are shown.
Abstract: The two cart inverted pendulum system is a good
bench mark for testing the performance of system dynamics and
control engineering principles. Devasia introduced this system to
study the asymptotic tracking problem for nonlinear systems. In this
paper the problem of asymptotic tracking of the two-cart with an
inverted-pendulum system to a sinusoidal reference inputs via
introducing a novel method for solving finite-horizon nonlinear
optimal control problems is presented. In this method, an iterative
method applied to state dependent Riccati equation (SDRE) to obtain
a reliable algorithm. The superiority of this technique has been shown
by simulation and comparison with the nonlinear approach.
Abstract: A numerical method for Riccati equation is presented in this work. The method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The operational matrices of derivative and product of hybrid functions are presented. These matrices together with the tau method are then utilized to transform the differential equation into a system of algebraic equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.
Abstract: In this article an evolutionary technique has been used
for the solution of nonlinear Riccati differential equations of fractional order. In this method, genetic algorithm is used as a tool for
the competent global search method hybridized with active-set algorithm for efficient local search. The proposed method has been
successfully applied to solve the different forms of Riccati
differential equations. The strength of proposed method has in its
equal applicability for the integer order case, as well as, fractional
order case. Comparison of the method has been made with standard
numerical techniques as well as the analytic solutions. It is found
that the designed method can provide the solution to the equation
with better accuracy than its counterpart deterministic approaches.
Another advantage of the given approach is to provide results on
entire finite continuous domain unlike other numerical methods
which provide solutions only on discrete grid of points.
Abstract: State-dependent Riccati equation based controllers are
becoming increasingly popular because of having attractive
properties like optimality, stability and robustness. This paper focuses
on the design of a roll autopilot for a fin stabilized and canard
controlled 122mm artillery rocket using state-dependent Riccati
equation technique. Initial spin is imparted to rocket during launch
and it quickly decays due to straight tail fins. After the spin phase, the
roll orientation of rocket is brought to zero with the canard deflection
commands generated by the roll autopilot. Roll autopilot has been
developed by considering uncoupled roll, pitch and yaw channels.
The canard actuator is modeled as a second-order nonlinear system.
Elements of the state weighing matrix for Riccati equation have been
chosen to be state dependent to exploit the design flexibility offered
by the Riccati equation technique. Simulation results under varying
conditions of flight demonstrate the wide operating range of the
proposed autopilot.
Abstract: State Dependent Riccati Equation (SDRE) approach is
a modification of the well studied LQR method. It has the capability of being applied to control nonlinear systems. In this paper the technique
has been applied to control the single inverted pendulum (SIP) which represents a rich class of nonlinear underactuated systems. SIP
modeling is based on Euler-Lagrange equations. A procedure is developed
for judicious selection of weighting parameters and constraint handling. The controller designed by SDRE technique here gives better results than existing controllers designed by energy based techniques.