Керування
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
, називається марковською позиційною стратегією (стратегією, кожний елемент якої залежить тільки від поточного стану системи).
Керування
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
, називається напівмарковською позиційною стратегією (стратегією, кожний елемент якої залежить тільки від поточного і початкового станів системи).
Марковські та напівмарковські позиційні стратегії використовуються найчастіше.
Зрозуміло, що в загальному випадку кінцевий стан системи
![](data:image/png;base64,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)
, згідно з формулою (2)
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
, залежить від початкового стану
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABUAAAAZCAYAAADe1WXtAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAD2SURBVEjHY2hsbGSgNmYYNZT+hjZEG/swGEctJNvQ+jwPQ1kGhjcMDAz/MbHsG4+8ekPquDQvTyKto4NncIUpOPyg3jWObvBBCRIZjz3EuhirYJQxw0KQIXl5Lraysh4rqeJ9uItJcB1BQ+vrYyWNGRjuwoKAqoZiS5+IZIc7iWE1NNrYuN7TU7aHgcH4bmx9vSSyZUYMsqdAhkEMNzqFLI/TUFB4grwN0SR7E2QAyBKQZuTc1dGRxuMhw7AHWxDBGTlussXgyEHThJy8wGqQggSUSmTdcoopSvwgQ5ENGbyGkhymxGCM2MeR20hO2GSn05FTRwEAWWYA2maBlZMAAAAASUVORK5CYII=)
, керувань
![](data:image/png;base64,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)
і збурень
![](data:image/png;base64,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)
. Щоб переконатися в цьому, досить виразити в (2)
![](data:image/png;base64,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)
через
![](data:image/png;base64,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)
, потім
![](data:image/png;base64,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)
через
![](data:image/png;base64,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)
і т.д. Якщо ці перетворення можливо провести, то одержимо співвідношення
![](data:image/png;base64,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)
. Це означає, що різним реалізаціям випадкового збурення
![](data:image/png;base64,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)
для одного початкового стану
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABUAAAAZCAYAAADe1WXtAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAD2SURBVEjHY2hsbGSgNmYYNZT+hjZEG/swGEctJNvQ+jwPQ1kGhjcMDAz/MbHsG4+8ekPquDQvTyKto4NncIUpOPyg3jWObvBBCRIZjz3EuhirYJQxw0KQIXl5Lraysh4rqeJ9uItJcB1BQ+vrYyWNGRjuwoKAqoZiS5+IZIc7iWE1NNrYuN7TU7aHgcH4bmx9vSSyZUYMsqdAhkEMNzqFLI/TUFB4grwN0SR7E2QAyBKQZuTc1dGRxuMhw7AHWxDBGTlussXgyEHThJy8wGqQggSUSmTdcoopSvwgQ5ENGbyGkhymxGCM2MeR20hO2GSn05FTRwEAWWYA2maBlZMAAAAASUVORK5CYII=)
відповідатимуть різні оптимальні стратегії керування
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAUCAYAAABSx2cSAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADKSURBVDjLY2hsbGQgFzMMTs0dHWk8HjIMe4yjG3zwaoYpZGBg+I8dG9+Nra+XJM1mj+hk2vs5yphhIW5ny77xyKs3xKq5IdrYB7dGApqjjGV7QZIgf7oZu9WmdXTw1NfHShoxyJ5C14TTzyANxnLusxCajXajhzJuzXkehrKyHivBmkFsBqNTRGsG+904aiHcIGI1wxKKrFtOMUKz7E2Qn/PcjFNwBhgI57jJFoNCFpYcwf5nYLhLVAqDaEZVBIt7bOl7kGZJmmoGAMyDrkkZ0hNnAAAAAElFTkSuQmCC)
.
4 Формальна постановка задачі оптимального стохастичного керування
Розглянемо систему (2) із цільовим функціоналом (3). Надалі, якщо інше не обговорено спеціально, будемо вважати, що оптимальні керування на кожному кроці позиційні:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAF0AAAAZCAYAAABTuCK5AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAKcSURBVGje7VkxTsMwFP0H4AAgxWwcgLorTMgYqTMSrTqBmJAZOqPQrQMcgG6MDJwAVhZuwMANuAPgpnYd13HsxA5FyeClavLff//5+fsHptMpdKvZ1XoCUkb3MWEXId85xOiesnS/I72AcITo0+VsthXyvbPZ5RZF6KmI+PYSno538O7xPDTh6vt70HsZp+lOR7q0AHjEo9tBzBhXBE0QuZp4k347wgPAw8dNIqwupkyF6N3muyFiLewLeu+62g1/gi8A+F5f6MsFZBTfDYyJKxAS+qpbS+hYC29P4FVXe7mqGNuO5XuVlV4DkyDCVb118+c2phe4nQcowKfJa2OdHQD4U7WYdf/iW0lRQbbl0MdfWIu0Ag10hjP/m69dmUiX+f8ucchKyzHYkTv+vDXlweDh/aIyCukLIBUD5qtt8snVKlJek6TrlsDY0UHdPt5KOvculp7t8a2ntlJ6Ef670oWabaRLxdcUWynppmSE/8XuZzfFXnTfD5F3Ken6SZvZwnqrlL1o5XubZC9l2HxIL9rhPvlbSdd7Sp5Yv99/KNpiI4zTKkprQuk2bGWEiudPTtBd1Rhl+MHUpeiHanpGD9VKxZ5b2FS1usBk6hlReq7iKMNW1qfzgvJYKh86wT75W/v03G1s+SdpCxpADozvCFOLFYt0uXhXsTzwTbbkgs10I5VxlrnK4hied82/8o3UXL1sXswIOY1tMZwMn4K6YPOZvdTJ32n24nqNJpjc0D48N3Gr85kG+mArmgCGjFE0LKs0gEqS5I0Qch3jA4DL9gyBzTbvDhGDYz/exfMg83Sx3dUtysbjgxjkC9Jdle6LTTQMMfJnBF8E+3Kkfv8TB21Tw6MY2Hzn5S4x+O+2uK2bMm7C6kjoSG/H+gFBM0cxHwkodwAAAABJRU5ErkJggg==)
,
![](data:image/png;base64,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)
і
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGUAAAAZCAYAAAAonOB1AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAALqSURBVGje7Zm9TtxAEMf3AXiAIHnpeABu09JFi5GokXLWVUFUaFNQI3PdFfACdJQUeYLQpuENKHgD3oFk7azP+GZmP8Y2lrhim7vzzfx2Zv47OxbL5VJs17TWqMZKkx8obc5inpkreZub8mDqGxnLRnGN6rSU+cP5arUT89xqdb6TS/kw5cCksFFc4zhdLnbV3tFdbEDaz8/E7PeiLHcnFxAGG8Y1iuNzJe5VcX3C+Y8LLS+lvricWlC4bBCX96HrQp0INb/nZNJMyKcQ+aFsVRIhZk99VkslIZl4FEK8rZd8bfta+dT6vr2BoWyxXMAPxOt7J2FnYzJBZPljt7xjbbkNHKJa3MZjGY/JDMTWB5ffYWO+pJ4FTSYGVprPlpUKKMDchSUO1VnFsMVyDX8ICvHSV3ZXzgv1MoiEEZtrtDrrZnifbF2uzYzpQNelnbYRrpQhx9ta7WSjKX0ka2v/YBmFz4d/y5PJziZ1WBdKlV1+jK0Prg8LSrd0jfl26Ov1saDENBNwcuDnZVURqihj2ThcgwbFZQ0VlCazAs4KLCiQvERJB2Hb+gdVkY+Nw/XhleK0OaTXh4KCylaAfIWcJ5B0hbBxuFhBqX9PtJIRQQnpYtCgJI5hfBuHSVdMUFK42JWCZVKoY/b542N5E1KNkH+c276vg6Jk0cfG4SIzf30RqqNY5PmPdxclz9zHJw9Or2s78rmyQQQZ039Oe4pVu7VF/R/FxuUCHWyW7R7K7/tVRgCHmjVuP4PaQOpi1tj5D9Q+FzAp8d3om8yNbImhUQrlB8XWF9eGkZjhmnsnYLQ+pSQstV0devbVx+WYy+adfcVMPG2EtdJX+VfxyycbfUx4uYPRoRaXDeJKHvjZCGdZ9kdr/dN3OeK+D7G+He2pu6m+T0llw7g2ghJaKU7q2iVsFotDaqgn1fw2BZxzORwlMIlsGBdjiLZ+x1wP1Oibe6oE+bqgqaxYNopr0qCfdW03YRuU7QpZfwENElqo3fJJdgAAAABJRU5ErkJggg==)
,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADgAAAAUCAYAAADY6P5TAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAHESURBVFjD7Vc7csIwEN0DcAFm2NwBRJ3SUcEFYg8VDBXjhgMYd264QDq6cIZwgtyAghtwhwTLkRH2riR7yGeIC834J+17u+9pZUjTFO553DW5/0VwHYkJiHDrmpAk0/4I8F3GyZB6n2WLnhzAXkTryZ8iWAAfvU2TpG+bYCZCkwGAD3qIo2u9tqMeG0950nMeQkQJKdFlgCsMlivbwqHADVe9MrCMZt9ZFUUC4GhiNQmb6rmeGMshotwtsqxHLux4/1MjLwQM5L6KQ5FE3JkFICoEW15y19kpSQOc9HN9TwEgE5Z/6xGnRvBLktV3kZQzM67VY/XN5dqj6lsN6jxH3XsQu4Bs51EtUVciSIJUmTUZzp8F2IKkF8AbSN0kaYvLZrdmYII0J1Of6t2qjZSWYpRj6XUXOSoCIty4tmzXDuzrc056OQ4RxPMmCrKC0EHMazIhz/IREQ5N/NemgpxNyhZBxLf75Fw1pfWHpxcOuO57xYbjt2m09SDXHko/NiGofTce4yuVNRXsLIk4EHN1glA+xEN+7ToMtN1FS2lXpFg8p9uGUxIcCK17TZ47SbjX9+y3xhGsPo9PVPe71BHsCP7u+ATFjlvLBSVnMQAAAABJRU5ErkJggg==)
.
За таких умов задача оптимального стохастичного керування полягає в пошуку оптимальної послідовності функцій керування
![](data:image/png;base64,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)
, (тобто стратегії керування), що мінімізує сумарні витрати за увесь час функціонування системи.
Формальна постановка задачі оптимального стохастичного керування зі скінченним горизонтом у дискретному випадку має вигляд:
![](data:image/png;base64,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)
, (4)
![](data:image/png;base64,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)
. (5)
Розв’язання задачі оптимального стохастичного керування з нескінченним горизонтом полягає в пошуку послідовності керувань
![](data:image/png;base64,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)
, які мінімізують сумарні витрати.
Формальна постановка задачі оптимального стохастичного керування з нескінченним горизонтом у дискретному випадку має вигляд:
![](data:image/png;base64,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)
, (6)
![](data:image/png;base64,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)
. (7)
Далі під час розв’язання задач оптимального керування вважатимемо, що границя у (6) існує для всіх
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAUCAYAAABSx2cSAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADKSURBVDjLY2hsbGQgFzMMTs0dHWk8HjIMe4yjG3zwaoYpZGBg+I8dG9+Nra+XJM1mj+hk2vs5yphhIW5ny77xyKs3xKq5IdrYB7dGApqjjGV7QZIgf7oZu9WmdXTw1NfHShoxyJ5C14TTzyANxnLusxCajXajhzJuzXkehrKyHivBmkFsBqNTRGsG+904aiHcIGI1wxKKrFtOMUKz7E2Qn/PcjFNwBhgI57jJFoNCFpYcwf5nYLhLVAqDaEZVBIt7bOl7kGZJmmoGAMyDrkkZ0hNnAAAAAElFTkSuQmCC)
і
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAZCAYAAAAxFw7TAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADzSURBVEjHY2hsbGSgJmYYNZD2BjZEG/swGEctJMvA+jwPQ1kGhjcMDAz/MbHsG4+8ekPKXZiXJ5HW0cEzOMIQHF5QLxpHN/igBIOMxx5iXIpVMMqYYSHIgLw8F1tZWY+VFHsZ7lIiXUXQwPr6WEljBoa7MG9TzUBc6Q+RvDCTElYDo42N6z09ZXsYGIzvxtbXSyLLdXSk8XjIyq4EGQS2WM59FnKwYA0/kFchrpC9CdIIsgBmMHrOAUUgctDADcpxky0GRwRUMdglMgx7kJMQTJ2sW04xLj7JCXfwG0h0GBKLUWIZFHFoOYmsAoDkdDi86xQAxpTb41YxOYQAAAAASUVORK5CYII=)
.
Будемо розглядати задачі (4) – (5) і (6) – (7) у стаціонарному випадку, тобто припускатимемо, що простори станів і керувань
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAUCAYAAACEYr13AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADBSURBVDjLY2hsbGSgBDMMYwM6OtJ4PGQY9jAwMPyHYNk3Hnn1hvX1sZLGxtH1eA0AK2JguCvrllOMzUDj6AYfvAbkuMkWM8h47Enr6ODBcJWs7EqQSwgbAHUyuly0h0cyssF4vYDuXJICEdkQBuOohWRHY5Qxw0KwIVjCBMOA+jwPQ2O3vBTsYYLdJSichmhjH+Sow4hCLK4gKvrg4UHIALh/0ZwKEccerai2QJMoyCuIJAzCxndj6+slR1p2JhYDAHam0OhZ6XyAAAAAAElFTkSuQmCC)
і
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAUCAYAAABroNZJAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADFSURBVDjLY2hsbGSgFDOMMENy3GSLGRgY/iOw8d3Y+nrJ+jwPQ2O3vBS8hsA1y3jsSevo4IGJ19fHShozMNwFyRlHN/jgNCTKmGEhSJGsW04xNnmQK2QZjE6BXITVEJgLcBkAd42c+yyYC7HYwPAG3QtYDTGOrscasMS4Am/sdHSk8XjIMOxhYJB945FXbzhwhiBihUJDGqKNfcBpwzhqIc5ABQW+cVQv3hQLSyPYYggc8FjEcdsGimqU5I471kZaUUAMBgDToO6PbnyehwAAAABJRU5ErkJggg==)
, обмеження керування
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACgAAAAYCAYAAACIhL/AAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAHaSURBVFjD1VexkcIwELwCaIAZRA/48g+NAhp4e4ieIWKcEP8IMic0QEZIDU8FdEBAB/Twj+2XEeJOkh/M8IFmENJJe3t7ujMsl0t45dHKoSqTA4yzSej+BMVKZmrwFIAFOCHkdprnnVCbPJ92pBBbCuRjwalxF/vDdRNwpm0E0ddYqW5rABOEDaaL0V/tZ7GYi3g2ZwEWFwDAtzlsg+IQar1iQOw5LV2Fswc7ypFSHhDtTRZpDQGcXExQOiuB9+TO/E+DsZ2+DDyaYPR+k5SbyxcpjmxDao/pQA0Ek01QQsj0wyUT01HvBmqkiMp0oEwOgKMtByoies7dUcnsQtBtFjIXXe3BVFEgbLsqGr/hPLNbzj3OVxoXJ61lIryXxdBHmAN4k1gBEnACrBbd+stinNgOaKY4gCGJ5wVYC90RgmJPjPGnve5jkMrOxgBD9Fcw5UoElsF3+SYEHHz6C2OQ0QlXikznKFv9rIQ8X5TMgMw66yJflaCcKy86z7VmK5bFofjt6l6872DNhuPFZz03DtaZq8NuVhUuWYIqyT2dTEgt9rZqvlp8z6C6kSajlJglr4f3g1wihdToYR/XrfaDdZgwWTW1owpAa98kVKh8jS4njZf+ovsXAH8AxYVs7p6U3pQAAAAASUVORK5CYII=)
, функція
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAYCAYAAAAcYhYyAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADLSURBVDjLY2hsbGSgFDMMTUNy3GSLGRgY/oOwrFtOMcmGRBkzLGSQ8diT1tHBAzYMyibaEIgLjO/G1tdLkuWd+jwPQ1kGhjfG0Q0+JIdJfX2spDEDw11YGKCHA0kuQfc/yYZ0dKTxeMgw7GEwjlpIdhQTEx4EDWmINvZhYJB945FXb0i2IeC0gSdqCRpCbHjgj2IiwwOvIYRSKVGGgMODCK/gNATiFaNTxLgCxRBIdBrfjazPUwUFKDFhgWEILCBBeYQUA4Zw8UhTQwAw9Vh4A+/jggAAAABJRU5ErkJggg==)
і витрати
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAUCAYAAACEYr13AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADFSURBVDjLY2hsbGSgBDMMXgNy3GSLGRgY/sOwrFtOMVEGdHSk8XjIMOxhYJB945FXbwgSq6+PlTRmYLgLM8w4usEHpwEN0cY+6IpAOMqYYSGDjMeetI4OHrwugDjd+G5sfb0kTAzuAmIMQHcBNi8RDET0AER3EUEDwK4wjlpIVjTW53kYyjIwvEEPRJLSATjEkb2AJfCwGgDzO7LtsEDFFrUoBkAU4g4skKuwpUYMv2MLPHyGYw1A1CgEYjwxMoizM90MAADaT8wdq3Lv1gAAAABJRU5ErkJggg==)
не змінюються при переході від кожного кроку до наступного. Якщо ж це не так, то задача є нестаціонарною. Нестаціонарна задача може бути зведена до стаціонарної за допомогою спеціальних методів, тому далі мова йтиме тільки про стаціонарні задачі.
Зупинимося детальніше на позначеннях, зроблених вище.
Визначення. Функція
![](data:image/png;base64,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)
називається функцією витрат за
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAYAAACNiR0NAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAEASURBVDjL7ZSxDcIwEEX/ABmASNwQcDtYKZggER1KFblJjZx0WYOSHZiADSjYgB1AdghcTBxSQJfiGlt++vfuEtR1jV8WZiCMTlYE3ADcbZEqyt692cYMXLt7W5xVm68Jq4w37QO+bo2J5V3T5FGyxAmcHia3rBXvlOK9n+DdBV0SbVaTgDaBYrXXlV64JMvklDdN1EvvnY0CnSfOjGxdpkwZB9/tKNBCOsBrCE9fnT9fwyjQ+pN+CkUlQDd71vpbn/1BBYGdP+lHpnQKBqYb3kPhT5b1ZlMS4RLyNwiU/oYXvm19EtAJJzqGHriUgXX5ALbihz8nmZKV3s2/r/8CH+PwRa5uSlo+AAAAAElFTkSuQmCC)
кроків при стратегії
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAUCAYAAABSx2cSAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADJSURBVDjLY2hsbGQgFzMMXs0dHWk8HjIMe4yjG3zwaoYpZGBg+I8dG9+Nra+XJM1mj+hk2vo5yphhIW4ny77xyKs3xKq5IdrYB7dGApqjjGV7QZIgP7oZu9WmdXTw1NfHShoxyJ5C14TTzyANxnLusxCajXYjhzB+zXkehrKyHivBmkFsBqNTRGsG+904aiHcIGI1wxKJrFtOMUKz7E2Qn/PcjFNwBhgI57jJFoNCFpYUwf5nYLiLLXXh0IyqCBb3BNP2MMrP+DAA34euSQaDJt8AAAAASUVORK5CYII=)
в задачі зі скінченним горизонтом
![](data:image/png;base64,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)
. Аналогом цієї величини для задачі з нескінченним горизонтом є функція
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABcAAAAZCAYAAADaILXQAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADoSURBVEjH7ZUxCoNAEEXnAF5AcA8h06dctrAOJGInVrKNBxjt9hopcwev4g28g2HXrEFINGZXSGExhSDPz+PPCE3TwF4DB/y/4CRFzAB6ABjsMF5W3pIrVQQighYAu4wo9KqFKAsRoNuS+Gt4nWICwHohKfYOLzmrflGyCp984/Xmvy0OvlfhLr5X4S6+Z/AxJQyY1okPJTO4SRmJtlAqsGD77AyfgHbVFxoy6nqdhE/vb05jQmBK+u4gl7n+kFXp7SpquLjQaRe45JjrinqHm81l7D7BsyznXJ69wE1tn01aWrTjH/p2HrFLUE52012FAAAAAElFTkSuQmCC)
– функція витрат при стратегії
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAUCAYAAABSx2cSAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADJSURBVDjLY2hsbGQgFzMMXs0dHWk8HjIMe4yjG3zwaoYpZGBg+I8dG9+Nra+XJM1mj+hk2vo5yphhIW4ny77xyKs3xKq5IdrYB7dGApqjjGV7QZIgP7oZu9WmdXTw1NfHShoxyJ5C14TTzyANxnLusxCajXYjhzB+zXkehrKyHivBmkFsBqNTRGsG+904aiHcIGI1wxKJrFtOMUKz7E2Qn/PcjFNwBhgI57jJFoNCFpYUwf5nYLiLLXXh0IyqCBb3BNP2MMrP+DAA34euSQaDJt8AAAAASUVORK5CYII=)
.
Для фіксованого стану
![](data:image/png;base64,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)
позначимо через
![](data:image/png;base64,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)
і
![](data:image/png;base64,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)
оптимальні витрати в цих задачах, тобто
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
.
Якщо останні співвідношення вірні для всіх
![](data:image/png;base64,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)
, то функція
![](data:image/png;base64,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)
називається оптимальною функцією витрат за
![](data:image/png;base64,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)
кроків, а
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABcAAAAZCAYAAADaILXQAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADQSURBVEjHY2hsbGSgFWYYNZwmhtfXx0oaMcie8sirN6Sa4R0daTweMgx7ZD2i693ljGfFxhqnMDAY342tr5ekmstz3GSLGRgY/jMYRy0cWi4nO8zr8zwMZRkY3oC9DcWybjnFVEstMO+je5kqhoO8bczAcJcUFxNteEO0sQ8Dg+wbbGFKseGQpEZ6kBA0HB7eWNIwxYZTEt4EDackvAkaTkl4oxgOcSXDf+PoBh9qBAmK4WBXynjsSevo4IEZDONTbDjcQFhWJzOFjFZzA2s4AEZKUjm8ZFZpAAAAAElFTkSuQmCC)
– оптимальною функцією витрат.
Стратегія
![](data:image/png;base64,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)
називається оптимальною при горизонті
![](data:image/png;base64,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)
в стані
![](data:image/png;base64,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)
, якщо
![](data:image/png;base64,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)
,
і оптимальною в стані
![](data:image/png;base64,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)
, якщо
![](data:image/png;base64,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)
.
Стратегія
![](data:image/png;base64,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)
називається оптимальною при горизонті
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAYAAACNiR0NAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAEASURBVDjL7ZSxDcIwEEX/ABmASNwQcDtYKZggER1KFblJjZx0WYOSHZiADSjYgB1AdghcTBxSQJfiGlt++vfuEtR1jV8WZiCMTlYE3ADcbZEqyt692cYMXLt7W5xVm68Jq4w37QO+bo2J5V3T5FGyxAmcHia3rBXvlOK9n+DdBV0SbVaTgDaBYrXXlV64JMvklDdN1EvvnY0CnSfOjGxdpkwZB9/tKNBCOsBrCE9fnT9fwyjQ+pN+CkUlQDd71vpbn/1BBYGdP+lHpnQKBqYb3kPhT5b1ZlMS4RLyNwiU/oYXvm19EtAJJzqGHriUgXX5ALbihz8nmZKV3s2/r/8CH+PwRa5uSlo+AAAAAElFTkSuQmCC)
, якщо
![](data:image/png;base64,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)
. Це означає, що стратегія
![](data:image/png;base64,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)
доставляє оптимальне значення цільовому функціоналу при всіх
![](data:image/png;base64,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)
.
Аналогічно, стратегія
![](data:image/png;base64,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)
називається оптимальною, якщо
![](data:image/png;base64,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)
. (8)
Стратегія
![](data:image/png;base64,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)
називається рівномірно оптимальною при горизонті
![](data:image/png;base64,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)
, якщо стратегія
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJsAAAAdCAYAAAC9iB5JAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAANeSURBVHja7Vs7UuQwENUBOMBShcg4ACPS3WjLOCCmanBNBEVEeQNiSkw2yV6AjAzOsJyAO3AD7rA7tsdGbkttSdZoNVMdvMTyuNU9T69bP7ZcLhnEanV7cH4snhZSHuraCQQMssxPOc9fb1erA/W59uW7jN+L4vGCAkfwxWMhLnh2d4+STcrFoTg+f4KsJBBcoMuOWlWDjCQQfAC5NGBjzvlrXspTr1y9VsUZ4+++v0/VVpJ10Q74X6VSdpS/tVlyWNix2bvrxKAm6RF743kha+lciBvGxMc2JhgxbaWannbFfzggBrKnMtFHNhljf5m4eo4h0bFspZqiUve/GxibVNprvBLs2afzpGykbFhfW04ZG6hmo5otBGoB22TL/pIHYx9jM9G66Isk3TFtJVtg77j/TbpvlBdMDtinSrb2WV0bDMA/Q46qmLaSVKo99b8hW9N/lGza0VaW32It+Ma0laSy7YH/k8hGIEwmW10frCVbJZuab/vvhZ/9xLSVem2zT/5bKxuRjchGZCOyEdko2OS/Hdk262zqus6+ka22kei6VaxYfy2x9JdT2pod1u1T46ldZ9PtIPgEwHd/1dWWq53U9xK37b8KuGep2rM9NGsbT+0OAmxQP9h2AI6KIs+vbZ2tv618y9T5qbaqQGYie9C9axqJWN+6QQj+WNfnY3ZC+I/5DtUty7Jf8Oh2IYR0UVEbZVP329HR0rG3xbqtlPOTOt1q5LaTYtMfoGkbjBQLWyY7PmQb61tXXgCFcX0+ZieE/7ZkK7Psci7Lk6o/HbmrfotChixL0FMf8Dyb612E9uPYb0wj1MUWZsdH2cb6Fho6OyH8tyFb/du8uIbxcEmhtvFEz7NBJyoJdOnA2OHLqj2fyx8mubW1Be30VAMCKrUhOFjfQsJkx9d/W9919lsy/CzL7ypJ0W/Cmh4jG7hlpWVrJXumInKM6ab3YT1oU7D62PGu2SYcGrWFyU4o/22UrUqhqhhUfeJnZy8iK29Cz+7ROwhfbJ/9gTndSto97y/YpF9bO1PS6P9CKP/HyKam0H7953eqBIun1e0qn1oNW7/ZRhrC7JgCrq4j7fIZMcx/jGymdTTfq5tj8bS6N2piJYHgotQ60jNsJuE6FSYQmjqQ/9ZlHQoOIRr+AdkP1FizUmuiAAAAAElFTkSuQmCC)
оптимальна при горизонті
![](data:image/png;base64,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)
для всіх
![](data:image/png;base64,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)
. Отже, якщо стратегія рівномірно оптимальна при горизонті
![](data:image/png;base64,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)
, то вона також оптимальна при горизонті
![](data:image/png;base64,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)
. Зворотне твердження в загальному випадку невірно.
Стратегія
![](data:image/png;base64,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)
називається стаціонарною стратегією, якщо
![](data:image/png;base64,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)
.
Якщо у цьому випадку значення цільового функціонала
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABcAAAAZCAYAAADaILXQAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADoSURBVEjH7ZUxCoNAEEXnAF5AcA8h06dctrAOJGInVrKNBxjt9hopcwev4g28g2HXrEFINGZXSGExhSDPz+PPCE3TwF4DB/y/4CRFzAB6ABjsMF5W3pIrVQQighYAu4wo9KqFKAsRoNuS+Gt4nWICwHohKfYOLzmrflGyCp984/Xmvy0OvlfhLr5X4S6+Z/AxJQyY1okPJTO4SRmJtlAqsGD77AyfgHbVFxoy6nqdhE/vb05jQmBK+u4gl7n+kFXp7SpquLjQaRe45JjrinqHm81l7D7BsyznXJ69wE1tn01aWrTjH/p2HrFLUE52012FAAAAAElFTkSuQmCC)
в задачі оптимального стохастичного керування з нескінченним горизонтом отримано з використанням стаціонарної стратегії
![](data:image/png;base64,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)
, то результат позначають
![](data:image/png;base64,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)
. Отже, стаціонарна стратегія
![](data:image/png;base64,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)
у задачі з нескінченним горизонтом оптимальна, якщо
![](data:image/png;base64,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)
. Тут
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABcAAAAZCAYAAADaILXQAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADQSURBVEjHY2hsbGSgFWYYNZwmhtfXx0oaMcie8sirN6Sa4R0daTweMgx7ZD2i693ljGfFxhqnMDAY342tr5ekmstz3GSLGRgY/jMYRy0cWi4nO8zr8zwMZRkY3oC9DcWybjnFVEstMO+je5kqhoO8bczAcJcUFxNteEO0sQ8Dg+wbbGFKseGQpEZ6kBA0HB7eWNIwxYZTEt4EDackvAkaTkl4oxgOcSXDf+PoBh9qBAmK4WBXynjsSevo4IEZDONTbDjcQFhWJzOFjFZzA2s4AEZKUjm8ZFZpAAAAAElFTkSuQmCC)
– оптимальне значення цільового функціонала задачі.