Global linearization of nonlinear systems - A survey

Čelikovský, Sergej

doi:10.4064/-32-1-123-137

Cited by 12 publications

(2 citation statements)

References 29 publications

(15 reference statements)

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“…It essentially cancels the non-linearities and transforms the system dynamics into a linear form. However, it is only applicable to systems that can be expressed in controllability canonical form [34] as follows:…”

Section: Discussionmentioning

confidence: 99%

“…It essentially cancels the non‐linearities and transforms the system dynamics into a linear form. However, it is only applicable to systems that can be expressed in controllability canonical form [34] as follows:

x^{false(σ false)} = f false(x false) + g false(x false) u

where x is the observed scalar output,

f false(x false)

and

g false(x false)

are non‐linear functions of x , u is the scalar control input, and

bold-italicx = false[x, \dot{x}, \dots x^{false(σ - 1 false)} {false]}^{T}

is the state vector. Then, the non‐linearities are cancelled using the control input

u = \frac{1}{g false(x false)} (v - f (x))

which implies

x^{false(σ false)} = v

Therefore, the linear control law can be designed with

v = - k_{0} x - k_{1} \dot{x} - \dots - k_{σ - 1} x^{false(σ - 1 false)}

such that the following dynamics is exponentially stable with roots strictly in the left‐hand‐side (LHS) of the complex plane:

x^{false(σ false)} + k_{σ - 1} x^{false(σ - 1 false)} + \dots + k_{0} x = 0

Taking the time derivative of (3) keeping

u_{p}

constant

x^{fals...}

…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Neural network‐based non‐linear adaptive controller design for a class of bilinear system

Bamgbose¹,

Li²,

Qian³

2020

Cognitive Computation and Systems

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This study presents a novel neural network (NN)-based non-linear adaptive control strategy for the global stability of multi-input-multi-output state-control homogeneous bilinear system (BLS) at the equilibrium position. Although this class of nonlinear system is neither piecewise nor feedback linearisable, conditionally stabilisable control system design can be utilised to generate multiple state transitions and corresponding control gains. The collected data was used to train a NN to obtain an optimal gain estimator. Then the optimal gain estimator was integrated into real-time control system operation to adaptively compute control gains, ensuring that the controller is continuously adjustable to changing behaviour of the system. The proposed design was shown, through an illustrative example, to overcome the stability limitations of traditional controllers for the investigated class of BLS. Furthermore, discussions about the utility of the traditional control and learning system integration, as well as stability analysis of the proposed scheme were presented.

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Section: Discussionmentioning

confidence: 99%