Nature-Inspired-Based Adaptive Neural Network Approximation for Uncertain System

Nature-Inspired-Based Adaptive Neural Network Approximation for Uncertain System

Uday Pratap Singh (Madhav Institute of Technology and Science, India), Sanjeev Jain (Shri Mata Vaishno Devi University, India), Akhilesh Tiwari (Madhav Institute of Technology and Science, India) and Rajeev Kumar Singh (Madhav Institute of Technology and Science, India)
DOI: 10.4018/978-1-5225-2990-3.ch019
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In this chapter, we focus and studied on some important nature inspired optimization methods like Particle Swarm Optimization (PSO), Firefly Algorithm (FA), Cuckoo Search (CS), Bat Algorithm (BA) and Flower Pollination Algorithm (FPA) are used for assign initial weights of Back-Propagation Neural Network (BPN). Success of neural networks are sturdily depends on different parameters and initialization weight is one, these nature inspired methods are used for optimization of mean square error (MSE) and mean absolute percentage error (MAPE) are used as test functions. The proposed method is based updating population, moving positions and obtain best solution space. The combination of nature inspired method and neural network were developed with the scope of creating an improved balance between premature convergence and stagnation. The performance of the proposed method is tested on two nonlinear systems. Results of FANN, CSNN, BANN and FPANN envisage that the proposed method exhibit high level of identification accuracy and its tracking error is closed in the neighbourhood of zero.
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Nonlinear System

Many systems in real world nature including biological process (Xie, 2006), chemical process (Watanbe, 1989) and control system (Chen, 1989) are highly nonlinear and uncertain. The dynamics of nonlinear systems is much wider than linear systems. Linear systems are described by set linear ordinary differential equations and often it is possible to find closed-form expressions for solution of such type of systems. In case of nonlinear system, it is not possible to make closed-form expression that the analysis of nonlinear systems in absence of closed-form is known as approximate or qualitative analysis. Some common nonlinear system models are given below:

  • 1.

    , where be the function at time t, known as state vector and is called input vector and . Model (1) is known as continuous time and its discrete time form is given by:

  • 2.

    : , model (2) represents first order difference equation. Then nth order difference equation is given by model (3)

  • 3.

    order differential or difference equation in model (3) can be represented via model (4).

  • 4.

    Model of the type (1) is known as forced system (it have an input) and model of the type (5) is known as unforced model.

  • 5.

    , is describing one of the following cases

    • a.

      There are no external input to the system, or

    • b.

      There is an fixed external input.

  • 6.

    Time-Invariant or Time-Varying System: A system is said to be time-invariant or autonomous if function depends on time, and a system is known as time-varying or non-autonomous if function g is not explicitly depends on time.

  • 7.

    Equilibrium Point: A point is said to equilibrium point for the system if . Model (5) represents a physical system then it should satisfy following conditions:

    • a.

      It has at least one solution i.e. existence of solution.

    • b.

      It has one solution for sufficiently small value of t, local existence of unique solution.

    • c.

      It has one solution for all values of t, global existence of unique solution.

    • d.

      It has global solution and solution depends on initial conditions.

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