Optimization of gear ratio with the objectives of fuel consumption reduction and vehicle longitudinal performance improvement has been the subject of many studies for years. Finding a strategy for changing gears with specific control objectives, especially in the design of vehicles equipped with Continuously Variable Transition system (CVT), which has advantage of arbitrary selection of gear ratio, has been the aim of some recent researches. Optimal control theory has rarely been used in the previous control approaches applied to such systems due to the limitations in the use of fast computational systems. The aim of this study is to design the aforementioned gear ratio change strategy and related control rules on the basis of optimal control. A driver model is also designed for the simulation of driving cycle using MATLAB Simulink Toolbar. Results of implementing optimal control rules in vehicle longitudinal movement simulation with the aim of fuel consumption reduction are finally represented. The presented method has the remarkable advantage of considerable fuel consumption reduction in comparison to other proposed approaches for gear ratio change strategies. 1. Introduction Continuously variable transmission (CVT) is an attractive technology and has become more practical with recent improvements in the technology. CVT is effective in achieving continuously smooth shifting and enables the engine to operate in its most efficient state. CVT has now reached a level that permits a large-scale usage of these devices even in a full-size passenger car class. Maximum torques of approximately 300？Nm can be handled with push belts (cf. Gesenhaus, 2000, or Goppelt, 2000). Other systems (e.g., toroidal drives), which cover even larger torque ranges, have been proposed as well. Although the efficiencies of CVT are inherently lower than those of cog wheel gear boxes, a more efficient total-system behavior can be obtained by shifting the engine operating points for a certain demanded power towards higher loads and lower speeds. A reliable method of control system design is usually trial and error in which different iterative methods are used for determining design parameters of an acceptable system. Appropriate performance of the system is usually introduced by some characteristics such as rising time, settling time, and overshoot or with some frequency characteristics such as phase margin, gain margin, and band width. With this method for multi-input multioutput systems, different criteria or performance characteristics for achieving the technological requirements
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