## Scientific Background of R&D:

- Unconventional methods in Computational Intelligence
- Applied advanced Soft computing and Stochastic fuzzy modeling with customer constraints
- Quantum computing and quantum algorithms (operators) with a new intelligence measure
- Quantum fuzzy inference model relative to quantum knowledge extraction and self-organization
- Robust intelligent fuzzy control based on mixed classical and quantum strategies of decision making

## Application:

Design of intelligent robust control for complex dynamic systems in unpredicted control situations

Modern control objects are complex dynamic systems that characterized by information uncertainty of model structures and control goals, a high degree of freedom and essential nonlinearities, instability, distributed sensors and actuators, high level of noise, abrupt jump changes in structure and dynamics, and so on. It is the typical information resources of unpredicted control situations. The structure design of robust advanced control systems for unpredicted control situations is the corner stone of modern control theory and systems. The degree to which a control system deals successfully with above difficulties depends on the *intelligent* level of advanced control system.

We are believed that R&D of sophisticated control technologies based on new types of computational intelligence has promoted automatic robust control to be at more and higher intelligent level. This problem is solved on the basic of developed information design technology of KB self-organization and a new computational intelligence methodology relative to quantum knowledge extraction (click corresponding key of section Technology).

At this page you can find overview of background (at first page) and details in tutorial (click corresponding keys) about Soft and Quantum Computing toolkit applied to information design technology of robust intelligent control systems.

## Advanced Soft Computing

*Soft Computing* (SC) applied to design of intelligent control systems represents a union of the following approaches: *Fuzzy Systems Theory* for a fuzzy control, *Genetic Algorithms* (GA) for global optimization of control laws, and *Fuzzy Neural Networks* (FNN) for implementation of fuzzy rules with possibility of learning by *back propagation* (BP) algorithm.

*Fuzzy systems* arose from the desire to describe complex systems behavior and decision making process with linguistic descriptions that are much closer to human feelings than exact numerical information. Fuzzy systems are based on *fuzzy sets theory* and *fuzzy control logic* introduced by L. Zadeh in 1965 and 1973, correspondingly. Later, it was proven that fuzzy systems can be considered as *“universal approximator”* of systems with undefined dynamics and structure. Therefore they became so attractive in control engineering.

For complex and ill-defined dynamic systems that are not easily controlled by traditional control systems (such as P(I)D controllers), especially in the presence of stochastic noises, *Fuzzy Controllers* (FC) and partially *FC-PID controllers* provide alternative way to design of robust control systems.

By using developed tools one can automatically derive the fuzzy “**if — then**” production rules (*Knowledge Base*) from a given experimental data or by *stochastic simulation* with mathematical model of control object.

*Genetic principles* of evolution are used in genetic optimizers today. Through the process of evolution, Nature has devised a useful method for optimizing large-scale nonlinear systems. A genetic optimizer running on a computer efficiently solves many previously difficult optimization problems by simulating the process of natural evolution. We are developed a new Genetic Algorithm (GA) with discrete constrains for optimization of designed knowledge base by using as fitness functions the information-thermodynamic and control criteria of dynamic object behavior [see details under corresponding key and Publications].

*Genetic Algorithm* (GA) with discrete constrains for optimization of designed knowledge base by using as fitness functions the information-thermodynamic and control criteria of dynamic object behavior [see details under corresponding key and Publications].

## Problems

Main problem in intelligent control systems design is following: how to introduce *self-learning, self-adaptation and self-organizing* capabilities into the control process that enhanced robustness of developed advanced control system. Many learning schemes based on BP-algorithm or other have been proposed. But for more complicated unpredicted control situations (time delay and noise in sensor system, jumped change of control object model parameters, unpredicted stochastic noises etc.), learning and adaptation methods based on BP-algorithms and other random iteration algorithms doesn’t can supply robust control in global sense.

The complexity of problem increased for the case of integrated control systems with the necessity to design the coordination control of many sub-systems as control objects with different optimization criteria (general problem of System of Engineering Systems). Soft computing methodologies had expanded application areas of FC by adding *learning and adaptation features*. But still now it is difficult to design “good” and robust intelligent control system, when its operational conditions have to evolve dramatically (aging, sensor failure, sensor’s noises or delay, etc.). Such conditions could be predicted from one hand, but it is difficult to cover such situations by a single FC.

One of the solutions seems obvious by preparation of a separate set of knowledge bases (KB-FC) for fixed conditions of control situations, but the following question raises:

*How to judge which KB-FC should be operational in the concrete time moment?*

At this moment the most important decision is a selection of the generalization strategy which will switch the flow of control signals from different FC, and if necessary will modify their output to fit present control object conditions. For this purpose the simplest way is to use a kind of *weighted aggregation of outputs* of each independent FC. But this solution will fail and distribution of weighting factors should be somehow dynamically decided.

Now it is obvious that new sophisticated technologies must be considered and developed. Our quantum control algorithm of knowledge base self-organization is based on special form of *quantum fuzzy inference* relative to quantum knowledge extraction from a few of Knowledge Bases designed by SC Optimizer tools.

Simulation results of increasing robustness in advanced control systems using the min-entropy principle of quantum knowledge extracted in on-line from a few (two or three) classical knowledge bases are demonstrated [see details here, and Simulation results].

## Quantum Principles and Advanced Quantum Computing

The *quantum principles* (such as quantum parallelism, quantum complementary, quantum long-distance correlation, quantum bio-inspired searching, etc) can be used for applications of quantum strategies for optimal decision making with conventional computers in much the same way that genetic principles of evolution are used in genetic optimizers. Nature also uses the principles of quantum mechanics to solve problems, including quantum-like optimization-type problems, searching-type problems, selection-type problems, etc.

*Quantum operators* The quantum operators, such as *superposition, entanglement* and *interference*, give rise to the quantum logic used in quantum computations. Moreover, the usefulness of these quantum operators gives rise to the new viewpoint on control and self-organization algorithms developed by our group (for details see the section Technology).

*Quantum information* In the classical computation one bit information is coded as 0 or 1. We can say also that one bit of information can represent the state 0 or the state 1.

In quantum computation quantum state information is used as a superposition of two states `C`

, and it is called as _{0}|0>+C_{1}|1>**qubit** (quantum bit).

With superposition operator for a given algorithm we can introduce all initial states that include the searching solutions, and accelerate computation processes by massive quantum parallelism.

The entanglement operator has no analog in classical computation. It allows physically set up statistical relations (quantum correlations) between solutions on the searching of space of the algorithm. In particular important case, it is the physical source of quantum oracle algorithms.

The interference operator performs division of solutions obtained by the quantum algorithm by finding a successful solution with maximal probability amplitude.

Quantum principles and quantum logic can be used with conventional computers if we find solutions to simulate and implement quantum algorithms on classical computers.

We describe solutions of these and other problems by providing method of simulation and design of quantum algorithms that can be efficiently simulated on classical computer [see details under corresponding key] (for details see in this section, Quantum Modeling System (QMS) and KeyLecture).

## Key points of Quantum & Soft Computing Application in Control Engineering

- PID Gain coefficient schedule (control laws) is described in the form of a Knowledge Base (KB) of a Fuzzy Inference System (realized in a Fuzzy Controller (FC))
- Genetic Algorithm (GA) with complicated Fitness Function is used for KB-FC forming
- KB-FC tuning is based on Fuzzy Neural Networks using error back propagation algorithm (step 1 technology)
- Optimization of KB-FC is based on SC optimizer (Step 2 technology)
- Quantum control algorithm of self-organization is developed based on the Quantum fuzzy inference model
- Quantum fuzzy inference model is realized for the KB self-organization to a new unpredicted control situation from a few designed KB in teaching conditions (Step 3 technology)

## QSC Optimizer Toolkit

*QSC Optimizer Toolkit* is based on Quantum & Soft Computing and includes the following:

- Soft computing and stochastic fuzzy simulation with information-thermodynamic criteria for robust Knowledge Bases design in the case of a few teaching control situations;
- Quantum Fuzzy Inference Model (QFIM) and its application to a KB self-organization from two or more knowledge bases for robust control in the case of unpredicted control situations.

## Simulations Results

Example of benchmark simulation results are available in this pdf.