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"... a: Zero mean white noise signal C(·): Controller transfer function e, E: Scalar error signal and a k×m matrix containing error signal values f(·): Arbitrary function F: Linear mapping matrix of dimension n×m G(·): Transfer function (for a process, closed loop system etc.) i,j: Indices for vector and ..."

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a: Zero mean white noise signal C(·): Controller transfer function e, E: Scalar error signal and a k×m matrix containing error signal values f(·): Arbitrary function F: Linear mapping matrix of dimension n×m G(·): Transfer function (for a process, closed loop system etc.) i,j: Indices for vector and matrix elements J(·): Cost function k: Number of data samples, i.e., local iteration steps K: Number of global iteration steps Kc: Critical gain of the controller KOL: Open loop gain of the process KP: Proportional gain of the PID controller L: Time lag, delay L(·): Filter transfer function m: Number of quality measures; dimension of output space M: Number of latent basis vectors in output oriented subspace n: Number of the parameters; dimension of input space N: Number of latent basis vectors in input oriented subspace q, Q: Quality measure vector and matrix, dimensions m×1 and k×m, respectively; shift operator r: Reference signal; setpoint R n: n-dimensional linear space s: Laplace variable t: Continuous or discrete time index Tc: Period of the critical oscillation TI: Integration time TD: Derivation time TR: Rise time TS: Settling time

### Towards a Systemic View of Complexity?

"... General System Theory concept is close to theory of control systems. In this chapter, we try to find a systematic view of complexity from the viewpoint of system concepts. The first part of the chapter covers about General System Theory from Bertalanffy’s book “General System Theory ” [1]. In this b ..."

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General System Theory concept is close to theory of control systems. In this chapter, we try to find a systematic view of complexity from the viewpoint of system concepts. The first part of the chapter covers about General System Theory from Bertalanffy’s book “General System Theory ” [1]. In this book he shows that reductionism is completely wrong and modelling the system from the holistic viewpoint is the correct approach. One approach to looking at complex systems in a systemic perspective and a way to control the emerging patterns as well is demonstrated. 14.1 General System Theory “System Theory ” represents a novel paradigm in scientific thinking [1]. General system theory is similar to “theory of evolution”, which comprises about everything between fossils digging, anatomy and the mathematical theory of selection, or behavior theory extending from bird watching to sophisticated