Research

• An Elementary Proof for the Existence of Limit Cycle in Three Gene Cyclic Regulatory Network:

Oscillatory networks are important in several biological contexts. However, establishing simple conditions for their existence is challenging, especially in higher dimensional models. Here, we apply an analytical technique to provide an elementary proof for the existence of oscillation in a benchmark cyclic three-dimensional oscillator. This analytical technique is based on the Brouwer's fixed point theorem. We establish the presence of a positively invariant region. A subset of this region is torus-like with the property that the flow maps a cross-section of the torus into itself. This leads to the existence of a limit cycle solution. These results should help in tracing the path of the limit cycle in the phase space.

• Decentralized Control of Multi-Input Multi-Output Processes Using Effective Transfer Function Method:

The design of controllers for multi-input multioutput systems are always complicated and difficult as compared to single-input single-output systems due to the interactions between inputs and outputs. These interactions are addressed in a quantitative manner using Interaction Measures. For ease of designing, the complex multi-input multi-output systems are assumed to be divided into several equivalent single loops and then the controllers are designed for these single loops differently. To simplify the tuning in case of failure tolerant systems, the decentralized controllers are used. The effective transfer function method is used for decentralized control of multi-input multi-output in this paper. This decentralized control method is compared with a centralized control which uses an interaction measure approach based on Hankel Interaction Index Array. Examples using both the methods are employed to show the effectiveness of the decentralized method over the centralized method. The effectiveness is shown by comparing the rise time, settling time and overshoot of the responses obtained from both the methods. 

• An Optimization-based Adaptive Sliding Mode Control for an Inverted Pendulum:

The work proposes an optimization-based robust adaptive gain sliding mode control technique to handle bounded behavior of uncertainties/perturbations without having the exact knowledge of the bound a priori. The constant of the sliding surface follows dynamical adaptive nature using three optimization techniques, i.e. Harmony Search Algorithm, Bacterial Foraging Optimization Algorithm and Gradient Search Algorithm to extenuate the extent of chattering. The gain of the switching control law, which is a part of the sliding mode control design, is calculated using the gain adaption technique. Lyapunov Stability Criterion is applied to assure the stability of the closed-loop system with adaptable gain and the optimized value of the sliding constant. An inverted Pendulum system has been taken to validate the proposition both in the simulation environment and the hardware platform.