Novel Design of a Model Reference Adaptive Controller for Soft Tissue Operations

Model Reference Adaptive Controllers (MRAC) have dual functionality: besides guaranteeing precise trajectory track- ing of the controlled system, they have to provide an “external control loop” with the illusion that it controls a physical system of prescribed dynamic properties, i.e., the “reference system”. The MRACs are designed traditionally by Lyapunov’s 2 nd method that is mathematically complicated, requiring strong skills from the designer. Adaptive controllers alternatively designed by the use of Robust Fixed Point Transformations (RFPT) operate according to Banach’s Fixed Point Theorem , and are normally simple iterative constructions that also have a standard variant for MRAC design. This controller assumes a single actuator that is driven adaptively. Master–Slave Systems form a distinct class of practical applications, in which two arms—the master and the slave—operate simultaneously. The movement of the master must be tracked precisely by the slave in spite of the quite different forces exerted by them. In the present paper, a soft tissue-cutting operation by a master–slave structure is simulated. The master arm has a simple torque–reference friction model, and is driven by the surgeon. The obtained master arm trajectory has to be precisely tracked by the electric DC motor driven slave system, which is in dynamic interaction with the actual tissue under operation. It is shown via simulations that the RFPT-based design can efficiently solve such tasks without considerable mathematical complexity

Nonlinear Model Predictive Control Using Robust Fixed Point Transformation-Based Phenomena for Controlling Tumor Growth

In this paper a novel control strategy is introduced in order to create optimal dosage profiles for individualized cancer treatment. This approach uses Nonlinear Model Predictive Control to construct optimal dosage protocols in conjunction with Robust Fixed Point Transformations which hinders the negative effect of inherent model uncertainties and measurement disturbances. The results are validated by extensive simulation on the proposed control algorithm from which conclusions were drawn

Observation-Based Data Driven Adaptive Control of an Electromechanical Device

The model-based approach in control engineering works well when a reliable plant model is available. However, in practice, reliable models seldom exist: instead, typical “levels” of limited reliability occur. For instance, Computed Torque Control (CTC) in robotics assumes almost perfect models. The Adaptive Inverse Dynamics Controller (AIDC) and the Slotine Li Adaptive Robot Controller (SLARC) assume absolutely correct analytical model form, and only allows imprecise knowledge regarding the actual values of the model parameters. Neglecting the effects of dynamically coupled subsystems, and allowing the action of unknown external disturbances means a higher level of corrupted model reliability. Friction-related problems are typical examples of this case. In the traditional control literature, such problems are tackled by either drastic “robust” or rather intricate “adaptive” solutions, both designed by the use of Lyapunov’s 2 nd method that is a complicated technique requiring advanced mathematical skills from the designer. As an alternative design methodology, the use of Robust Fixed Point Transformations (RFPT) was suggested, which concentrates on guaranteeing the prescribed details of tracking error relaxation via generation of iterative control signal sequences that converge on the basis of Banach’s Fixed Point Theorem . This approach is essentially based on the fresh data collected by observing the behavior of the controlled systems, rather than in the case of the traditional ones. For the first time, this technique is applied for order reduction in the adaptive control of a strongly nonlinear plant with significant model imprecisions: the control of a DC motor driven arm in dynamic interaction with a nonlinear environment is demonstrated via numerical simulations

Preliminary investigations on the applicability of the fixed point transformations-based adaptive control for time-delayed systems

In this paper, for the first time, a possible tackling of the problem of known time-delay by the use of a Fixed Point Transformation-based adaptive controller is investigated. This approach at first transform the control task into a fixed point problem then solves it via iteration. The preliminary results that were obtained by numerical simulations for a strongly nonlinear controlled system, a van der Pol oscillator, are promising. It is expedient to make further, systematic investigations